#definiere erste Funktion
def f(x):
return (exp(-x^2))/(sqrt((1+x^4)))
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#definiere gleichverteilte Stützstellen
def stst(x,n):
return -5+(10)*x/n
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#definiere die Li
def Li(j,n):
sum=1;
for i in range(n+1):
if(i != j):
sum*=(x-stst(i,n))/(stst(j,n)-stst(i,n))
return sum
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#definiere Interpolationspolynom mit gleichverteilten Stützstellen
def pn(f,n):
poly=0;
for j in range(n+1):
poly+= f(stst(j,n))*Li(j,n)
return poly
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#############################################################################################################################################
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#def Tschebyscheff Nst für n+1 Tschebyscheff-Polynom und transformiere sie auf Intervall [-5,5]
def tscheb(x,n):
return (5*(cos((2*x+1)/(n+1)*pi/2))).n()
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#definiere Li mit Tschebyscheff NST
def Litscheb(j,n):
sum=1;
for i in range(n+1):
if(i != j):
sum*=(x-tscheb(i,n))/(tscheb(j,n)-tscheb(i,n))
return sum
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#definiere Interpolationspolynom mit Tschebyscheff NST
def pntscheb(f,n):
poly=0;
for j in range(n+1):
poly+= f(tscheb(j,n))*Litscheb(j,n)
return poly
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#############################################################################################################################################
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#definiere Fehler für Gleichverteilte Stützstellen
def fehler(n):
poly= pn(f,n)
print 'Der Fehler ist:', sqrt(integral(((exp(-x^2))/(sqrt((1+x^4))) - poly)^2,x,-5,5).n())
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#Ausgabe für gleichverteilte Stützstellen
for i in range(1,5):
print 'Polynom bei n=',2^i,'ist:', view(factor(pn(f,2^i)))
print 'Der Fehler ist:', fehler(2^i)
Polynom bei n= 2 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{15650} \, {\left(\sqrt{626} x^{2} e^{25} - x^{2} - 25 \, \sqrt{626} e^{25}\right)} \sqrt{626} e^{\left(-25\right)} None Der Fehler ist: Der Fehler ist: 1.84169476474204 None Polynom bei n= 4 ist: \newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{752373750} \, {\left(12 \, \sqrt{626} \sqrt{641} x^{4} e^{\frac{101}{4}} - 64 \, \sqrt{626} x^{4} e^{19} + 4 \, \sqrt{641} x^{4} e^{\frac{1}{4}} - 375 \, \sqrt{626} \sqrt{641} x^{2} e^{\frac{101}{4}} + 1600 \, \sqrt{626} x^{2} e^{19} - 25 \, \sqrt{641} x^{2} e^{\frac{1}{4}} + 1875 \, \sqrt{626} \sqrt{641} e^{\frac{101}{4}}\right)} \sqrt{626} \sqrt{641} e^{\left(-\frac{101}{4}\right)} None Der Fehler ist: Der Fehler ist: 1.23787927079932 None Polynom bei n= 8 ist: \newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2213270512009839843750} \, {\left(35840 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{8} e^{\frac{413}{16}} - 131072 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{8} e^{\frac{47}{4}} - 917504 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{8} e^{\frac{97}{4}} + 114688 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{8} e^{\frac{313}{16}} + 1024 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{8} e^{\frac{13}{16}} - 1680000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{6} e^{\frac{413}{16}} + 4300800 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{6} e^{\frac{47}{4}} + 41574400 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{6} e^{\frac{97}{4}} - 4659200 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{6} e^{\frac{313}{16}} - 22400 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{6} e^{\frac{13}{16}} + 23887500 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{4} e^{\frac{413}{16}} - 26880000 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{4} e^{\frac{47}{4}} - 546560000 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{4} e^{\frac{97}{4}} + 47320000 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{4} e^{\frac{313}{16}} + 122500 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{4} e^{\frac{13}{16}} - 112109375 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{2} e^{\frac{413}{16}} + 32000000 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{2} e^{\frac{47}{4}} + 2016000000 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{2} e^{\frac{97}{4}} - 63000000 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{2} e^{\frac{313}{16}} - 140625 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{2} e^{\frac{13}{16}} + 123046875 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} e^{\frac{413}{16}}\right)} \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} e^{\left(-\frac{413}{16}\right)} None Der Fehler ist: Der Fehler ist: 2.08451729933186 None Polynom bei n= 16 ist: \newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{268898189279931824650511359767595044897422790527343750} \, {\left(110552458199040 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{1701}{64}} - 17592186044416 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{16} e^{\frac{119}{16}} - 615726511554560 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{16} e^{\frac{269}{16}} - 4802666790125568 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{369}{16}} + 32985348833280 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{801}{64}} - 12578413021757440 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{419}{16}} + 2201222278807552 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{1601}{64}} + 125069447659520 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{1301}{64}} + 17179869184 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{101}{64}} - 8809649012736000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{1701}{64}} + 1065151889408000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{14} e^{\frac{119}{16}} + 43052752175104000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{14} e^{\frac{269}{16}} + 365828134404096000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{369}{16}} - 2164663517184000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{801}{64}} + 997428845084672000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{419}{16}} - 171970490531840000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{1601}{64}} - 9184787562496000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{1301}{64}} - 939524096000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{101}{64}} + 277022166220800000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{1701}{64}} - 23694797701120000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{12} e^{\frac{119}{16}} - 1122449437491200000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{12} e^{\frac{269}{16}} - 10748399934504960000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{369}{16}} + 52214051635200000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{801}{64}} - 31129345825177600000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{419}{16}} + 5247115240407040000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{1601}{64}} + 255993892044800000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{1301}{64}} + 19561185280000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{101}{64}} - 4409574174720000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{1701}{64}} + 248161239040000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{10} e^{\frac{119}{16}} + 13597886382080000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{10} e^{\frac{269}{16}} + 153775248506880000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{369}{16}} - 581417041920000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{801}{64}} + 489551649832960000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{419}{16}} - 79600903782400000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{1601}{64}} - 3388647342080000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{1301}{64}} - 196218880000000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{101}{64}} + 37938579822000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{1701}{64}} - 1287195852800000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{8} e^{\frac{119}{16}} - 78508638208000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{8} e^{\frac{269}{16}} - 1107527771750400000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{369}{16}} + 3143492352000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{801}{64}} - 4125336190976000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{419}{16}} + 631022866073600000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{1601}{64}} + 21741367648000000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{1301}{64}} + 990189200000000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{101}{64}} - 174671953706250000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{1701}{64}} + 3157772800000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{6} e^{\frac{119}{16}} + 206156787200000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{6} e^{\frac{269}{16}} + 3694520793600000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{369}{16}} - 7911212400000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{801}{64}} + 18262327283200000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{419}{16}} - 2491939450000000000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{1601}{64}} - 61725127100000000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{1301}{64}} - 2389318750000000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{101}{64}} + 399464495815429687500 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{1701}{64}} - 3124944000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{4} e^{\frac{119}{16}} - 211584240000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{4} e^{\frac{269}{16}} - 4365156432000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{369}{16}} + 7936117500000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{801}{64}} - 38316461040000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{419}{16}} + 4060126570500000000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{1601}{64}} + 66137385234375000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{1301}{64}} + 2343875976562500 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{101}{64}} - 380968221038818359375 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{1701}{64}} + 810000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{2} e^{\frac{119}{16}} + 55566000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{2} e^{\frac{269}{16}} + 1203930000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{369}{16}} - 2067187500000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{801}{64}} + 28378350000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{419}{16}} - 1241552812500000000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{1601}{64}} - 17635693359375000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{1301}{64}} - 605621337890625 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{101}{64}} + 97429332733154296875 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} e^{\frac{1701}{64}}\right)} \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} e^{\left(-\frac{1701}{64}\right)} None Der Fehler ist: Der Fehler ist: 0.560438645356714 None Polynom bei n= 2 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{15650} \, {\left(\sqrt{626} x^{2} e^{25} - x^{2} - 25 \, \sqrt{626} e^{25}\right)} \sqrt{626} e^{\left(-25\right)} None Der Fehler ist: Der Fehler ist: 1.84169476474204 None Polynom bei n= 4 ist: \newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{752373750} \, {\left(12 \, \sqrt{626} \sqrt{641} x^{4} e^{\frac{101}{4}} - 64 \, \sqrt{626} x^{4} e^{19} + 4 \, \sqrt{641} x^{4} e^{\frac{1}{4}} - 375 \, \sqrt{626} \sqrt{641} x^{2} e^{\frac{101}{4}} + 1600 \, \sqrt{626} x^{2} e^{19} - 25 \, \sqrt{641} x^{2} e^{\frac{1}{4}} + 1875 \, \sqrt{626} \sqrt{641} e^{\frac{101}{4}}\right)} \sqrt{626} \sqrt{641} e^{\left(-\frac{101}{4}\right)} None Der Fehler ist: Der Fehler ist: 1.23787927079932 None Polynom bei n= 8 ist: \newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2213270512009839843750} \, {\left(35840 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{8} e^{\frac{413}{16}} - 131072 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{8} e^{\frac{47}{4}} - 917504 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{8} e^{\frac{97}{4}} + 114688 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{8} e^{\frac{313}{16}} + 1024 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{8} e^{\frac{13}{16}} - 1680000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{6} e^{\frac{413}{16}} + 4300800 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{6} e^{\frac{47}{4}} + 41574400 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{6} e^{\frac{97}{4}} - 4659200 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{6} e^{\frac{313}{16}} - 22400 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{6} e^{\frac{13}{16}} + 23887500 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{4} e^{\frac{413}{16}} - 26880000 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{4} e^{\frac{47}{4}} - 546560000 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{4} e^{\frac{97}{4}} + 47320000 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{4} e^{\frac{313}{16}} + 122500 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{4} e^{\frac{13}{16}} - 112109375 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} x^{2} e^{\frac{413}{16}} + 32000000 \, \sqrt{626} \sqrt{641} \sqrt{881} x^{2} e^{\frac{47}{4}} + 2016000000 \, \sqrt{626} \sqrt{641} \sqrt{50881} x^{2} e^{\frac{97}{4}} - 63000000 \, \sqrt{626} \sqrt{881} \sqrt{50881} x^{2} e^{\frac{313}{16}} - 140625 \, \sqrt{641} \sqrt{881} \sqrt{50881} x^{2} e^{\frac{13}{16}} + 123046875 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} e^{\frac{413}{16}}\right)} \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} e^{\left(-\frac{413}{16}\right)} None Der Fehler ist: Der Fehler ist: 2.08451729933186 None Polynom bei n= 16 ist: \newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{268898189279931824650511359767595044897422790527343750} \, {\left(110552458199040 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{1701}{64}} - 17592186044416 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{16} e^{\frac{119}{16}} - 615726511554560 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{16} e^{\frac{269}{16}} - 4802666790125568 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{369}{16}} + 32985348833280 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{801}{64}} - 12578413021757440 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{419}{16}} + 2201222278807552 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{1601}{64}} + 125069447659520 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{1301}{64}} + 17179869184 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{16} e^{\frac{101}{64}} - 8809649012736000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{1701}{64}} + 1065151889408000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{14} e^{\frac{119}{16}} + 43052752175104000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{14} e^{\frac{269}{16}} + 365828134404096000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{369}{16}} - 2164663517184000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{801}{64}} + 997428845084672000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{419}{16}} - 171970490531840000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{1601}{64}} - 9184787562496000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{1301}{64}} - 939524096000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{14} e^{\frac{101}{64}} + 277022166220800000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{1701}{64}} - 23694797701120000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{12} e^{\frac{119}{16}} - 1122449437491200000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{12} e^{\frac{269}{16}} - 10748399934504960000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{369}{16}} + 52214051635200000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{801}{64}} - 31129345825177600000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{419}{16}} + 5247115240407040000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{1601}{64}} + 255993892044800000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{1301}{64}} + 19561185280000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{12} e^{\frac{101}{64}} - 4409574174720000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{1701}{64}} + 248161239040000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{10} e^{\frac{119}{16}} + 13597886382080000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{10} e^{\frac{269}{16}} + 153775248506880000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{369}{16}} - 581417041920000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{801}{64}} + 489551649832960000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{419}{16}} - 79600903782400000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{1601}{64}} - 3388647342080000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{1301}{64}} - 196218880000000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{10} e^{\frac{101}{64}} + 37938579822000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{1701}{64}} - 1287195852800000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{8} e^{\frac{119}{16}} - 78508638208000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{8} e^{\frac{269}{16}} - 1107527771750400000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{369}{16}} + 3143492352000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{801}{64}} - 4125336190976000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{419}{16}} + 631022866073600000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{1601}{64}} + 21741367648000000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{1301}{64}} + 990189200000000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{8} e^{\frac{101}{64}} - 174671953706250000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{1701}{64}} + 3157772800000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{6} e^{\frac{119}{16}} + 206156787200000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{6} e^{\frac{269}{16}} + 3694520793600000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{369}{16}} - 7911212400000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{801}{64}} + 18262327283200000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{419}{16}} - 2491939450000000000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{1601}{64}} - 61725127100000000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{1301}{64}} - 2389318750000000 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{6} e^{\frac{101}{64}} + 399464495815429687500 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{1701}{64}} - 3124944000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{4} e^{\frac{119}{16}} - 211584240000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{4} e^{\frac{269}{16}} - 4365156432000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{369}{16}} + 7936117500000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{801}{64}} - 38316461040000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{419}{16}} + 4060126570500000000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{1601}{64}} + 66137385234375000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{1301}{64}} + 2343875976562500 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{4} e^{\frac{101}{64}} - 380968221038818359375 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{1701}{64}} + 810000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} x^{2} e^{\frac{119}{16}} + 55566000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{1504721} x^{2} e^{\frac{269}{16}} + 1203930000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{369}{16}} - 2067187500000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{801}{64}} + 28378350000000000000000 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{419}{16}} - 1241552812500000000000 \, \sqrt{626} \sqrt{641} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{1601}{64}} - 17635693359375000000 \, \sqrt{626} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{1301}{64}} - 605621337890625 \, \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} x^{2} e^{\frac{101}{64}} + 97429332733154296875 \, \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} e^{\frac{1701}{64}}\right)} \sqrt{626} \sqrt{641} \sqrt{881} \sqrt{4721} \sqrt{50881} \sqrt{54721} \sqrt{394721} \sqrt{1504721} e^{\left(-\frac{1701}{64}\right)} None Der Fehler ist: Der Fehler ist: 0.560438645356714 None |
#Fehler steigt am Rand stark an.
Funktion1=plot((exp(-x^2))/(sqrt((1+x^4))),-5,5)
PnMit2Stst=plot(pn(f,2),-5,5,color='yellow')
PnMit8Stst=plot(pn(f,8),-5,5,color='red')
PnMit16Stst=plot(pn(f,16),-5,5,color='black')
PnMit32Stst=plot(pn(f,32),-5,5,color='green')
PnMit64Stst=plot(pn(f,64),-5,5,color='purple')
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show(Funktion1+PnMit2Stst+PnMit8Stst+PnMit16Stst)
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show(PnMit32Stst)
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show(PnMit64Stst)
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#############################################################################################################################################
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#definiere Fehler für Tschebyschef Stützstellen
def fehlertscheb(n):
poly= pntscheb(f,n)
print 'Der Fehler ist:', sqrt(integral(((exp(-x^2))/(sqrt((1+x^4))) - poly)^2,x,-5,5).n())
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#Ausgabe für Tschebyscheff Stützstellen
for i in range(1,5):
print 'Polynom bei n=',2^i,'ist:', pntscheb(f,2^i)
print 'Der Fehler ist:', fehlertscheb(2^i)
Polynom bei n= 2 ist: (-0.230940107675850*x + 1.00000000000000)*(0.230940107675850*x + 1.00000000000000) - (8.84829859138229e-11)*(-0.115470053837925*x + 0.500000000000000)*x + (8.84829859138229e-11)*(0.115470053837925*x + 0.500000000000000)*x Der Fehler ist: Der Fehler ist: 1.65537028244 None Polynom bei n= 4 ist: (6.94090694647205e-6)*(-0.550552768188470*x + 2.61803398874990)*(0.129967878493163*x + 0.618033988749895)*(0.170130161670408*x + 0.500000000000000)*x - (1.40433438138665e-12)*(-0.550552768188469*x - 1.61803398874989)*(-0.129967878493163*x + 0.381966011250105)*(-0.105146222423827*x + 0.500000000000000)*x + (-0.340260323340816*x + 1.00000000000000)*(-0.210292444847653*x + 1.00000000000000)*(0.210292444847653*x + 1.00000000000000)*(0.340260323340816*x + 1.00000000000000) - (6.94090694647209e-6)*(-0.170130161670408*x + 0.500000000000000)*(-0.129967878493163*x + 0.618033988749895)*(0.550552768188469*x + 2.61803398874989)*x + (1.40433438138665e-12)*(0.105146222423827*x + 0.500000000000000)*(0.129967878493163*x + 0.381966011250105)*(0.550552768188470*x - 1.61803398874990)*x Der Fehler ist: Der Fehler ist: 1.06191869596 None Polynom bei n= 8 ist: -(2.46998334944342e-13)*(-1.68375184781447*x - 7.29085936938159)*(-0.584760880032618*x - 1.87938524157182)*(-0.311144765372083*x - 0.532088886237956)*(-0.150735449979618*x + 0.257772801031441)*(-0.122880664680917*x + 0.394930843634698)*(-0.108059442994933*x + 0.467911113762044)*(-0.101542661188575*x + 0.500000000000000)*x + (8.84829859138229e-11)*(-1.68375184781447*x + 8.29085936938159)*(0.108059442994933*x + 0.532088886237956)*(0.115470053837925*x + 0.500000000000000)*(0.132554530093763*x + 0.426022047760462)*(0.165556671665602*x + 0.283118582857949)*(0.381675557655469*x - 0.652703644666140)*(0.895905645404700*x - 2.87938524157182)*x - (8.84829859138229e-11)*(-0.895905645404700*x - 2.87938524157182)*(-0.381675557655469*x - 0.652703644666139)*(-0.165556671665602*x + 0.283118582857949)*(-0.132554530093763*x + 0.426022047760462)*(-0.115470053837925*x + 0.500000000000000)*(-0.108059442994933*x + 0.532088886237956)*(1.68375184781447*x + 8.29085936938159)*x + (9.79177286950834e-7)*(-0.895905645404700*x + 3.87938524157182)*(-0.584760880032618*x + 2.87938524157182)*(0.122880664680917*x + 0.605069156365302)*(0.132554530093763*x + 0.573977952239538)*(0.155572382686041*x + 0.500000000000000)*(0.203085322377149*x + 0.347296355333861)*(0.664965537728850*x - 1.13715804260326)*x + 0.0101590366730642*(-0.664965537728850*x + 2.13715804260326)*(-0.381675557655469*x + 1.65270364466614)*(-0.311144765372083*x + 1.53208888623796)*(0.150735449979618*x + 0.742227198968559)*(0.165556671665602*x + 0.716881417142051)*(0.203085322377149*x + 0.652703644666139)*(0.292380440016309*x + 0.500000000000000)*x - (9.79177286950834e-7)*(-0.664965537728849*x - 1.13715804260326)*(-0.203085322377149*x + 0.347296355333861)*(-0.155572382686041*x + 0.500000000000000)*(-0.132554530093763*x + 0.573977952239538)*(-0.122880664680917*x + 0.605069156365302)*(0.584760880032618*x + 2.87938524157182)*(0.895905645404700*x + 3.87938524157182)*x + (-0.584760880032617*x + 1.00000000000000)*(-0.311144765372082*x + 1.00000000000000)*(-0.230940107675850*x + 1.00000000000000)*(-0.203085322377149*x + 1.00000000000000)*(0.203085322377149*x + 1.00000000000000)*(0.230940107675850*x + 1.00000000000000)*(0.311144765372082*x + 1.00000000000000)*(0.584760880032618*x + 1.00000000000000) - 0.0101590366730642*(-0.292380440016309*x + 0.500000000000000)*(-0.203085322377149*x + 0.652703644666139)*(-0.165556671665602*x + 0.716881417142052)*(-0.150735449979618*x + 0.742227198968559)*(0.311144765372083*x + 1.53208888623796)*(0.381675557655469*x + 1.65270364466614)*(0.664965537728849*x + 2.13715804260326)*x + (2.46998334944342e-13)*(0.101542661188575*x + 0.500000000000000)*(0.108059442994933*x + 0.467911113762044)*(0.122880664680917*x + 0.394930843634698)*(0.150735449979618*x + 0.257772801031441)*(0.311144765372083*x - 0.532088886237956)*(0.584760880032618*x - 1.87938524157182)*(1.68375184781447*x - 7.29085936938159)*x Der Fehler ist: Der Fehler ist: 0.458252697981 None Polynom bei n= 16 ist: -(1.39116348212640e-13)*(-5.89822034704794*x - 28.3652978943719)*(-1.98864711312199*x - 8.90081947563013)*(-1.01154706764686*x - 4.03615993093503)*(-0.621043694228700*x - 2.09197215658020)*(-0.426164802796190*x - 1.12173429439100)*(-0.315212546742269*x - 0.569339527941365)*(-0.246310072378424*x - 0.226296785164499)*(-0.169565718456703*x + 0.155788095023197)*(-0.147386558948727*x + 0.266210830641147)*(-0.131391684898735*x + 0.345844044326706)*(-0.119801382250976*x + 0.403548346626591)*(-0.111498170594522*x + 0.444887304723300)*(-0.105769880927785*x + 0.473406573687743)*(-0.102168014489779*x + 0.491339081241606)*(-0.100428409891567*x + 0.500000000000000)*x + (8.11253701429134e-13)*(-5.89822034704794*x + 29.3652978943719)*(0.102168014489779*x + 0.508660918758394)*(0.103968947708782*x + 0.500000000000000)*(0.107701234122242*x + 0.482050956099341)*(0.113646509786701*x + 0.453459363150300)*(0.122285170857631*x + 0.411914934446805)*(0.134385318986365*x + 0.353723770664777)*(0.151163889081916*x + 0.273033475796407)*(0.174584790951008*x + 0.160399355776772)*(0.257044257601952*x - 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0.299135889752379)*(0.457901077385086*x - 0.827064740717406)*(0.736417521485310*x - 1.93836934308147)*(1.60873111614558*x - 5.41897572372971)*x - (1.91376264845534e-9)*(-1.60873111614558*x - 5.41897572372971)*(-0.736417521485311*x - 1.93836934308147)*(-0.457901077385086*x - 0.827064740717405)*(-0.325590938476360*x - 0.299135889752379)*(-0.203714376147746*x + 0.187162091947259)*(-0.172524016099451*x + 0.311614315165324)*(-0.151006147525352*x + 0.397472464247740)*(-0.135896073174961*x + 0.457762962433225)*(-0.125310577994431*x + 0.500000000000000)*(-0.118120896028971*x + 0.528687450335515)*(-0.113646509786701*x + 0.546540636849700)*(-0.111498170594522*x + 0.555112695276700)*(1.01154706764686*x + 5.03615993093503)*(1.22093849031025*x + 5.87164974358555)*(2.05875556467176*x + 9.21461203683559)*x + (3.07774848688181e-7)*(-1.60873111614558*x + 6.41897572372971)*(-0.903066439136245*x + 4.04195962984748)*(-0.694131122510105*x + 3.33816556677276)*(-0.621043694228700*x + 3.09197215658020)*(0.119801382250976*x + 0.596451653373409)*(0.122285170857631*x + 0.588085065553195)*(0.127481187465585*x + 0.570582396787725)*(0.135896073174961*x + 0.542237037566775)*(0.148434980904320*x + 0.500000000000000)*(0.166648917650934*x + 0.438646750800759)*(0.193248420073033*x + 0.349046906276087)*(0.233251068393370*x + 0.214298856737408)*(0.408208146683868*x - 0.375040250609783)*(0.640094268046196*x - 1.15614359952927)*(1.35810996015672*x - 3.57476381875291)*x - (3.07774848688181e-7)*(-1.35810996015672*x - 3.57476381875291)*(-0.640094268046196*x - 1.15614359952927)*(-0.408208146683868*x - 0.375040250609783)*(-0.233251068393370*x + 0.214298856737408)*(-0.193248420073033*x + 0.349046906276087)*(-0.166648917650934*x + 0.438646750800758)*(-0.148434980904320*x + 0.500000000000000)*(-0.135896073174961*x + 0.542237037566775)*(-0.127481187465585*x + 0.570582396787725)*(-0.122285170857631*x + 0.588085065553195)*(-0.119801382250976*x + 0.596451653373409)*(0.621043694228700*x + 3.09197215658020)*(0.694131122510105*x + 3.33816556677276)*(0.903066439136245*x + 4.04195962984749)*(1.60873111614558*x + 6.41897572372971)*x + 0.0000531711111847144*(-1.35810996015672*x + 4.57476381875291)*(-0.736417521485310*x + 2.93836934308147)*(-0.542400639798687*x + 2.42768570977642)*(-0.459354604630914*x + 2.20909519021762)*(-0.426164802796190*x + 2.12173429439100)*(0.131391684898735*x + 0.654155955673294)*(0.134385318986365*x + 0.646276229335223)*(0.140687000232418*x + 0.629689190894607)*(0.151006147525352*x + 0.602527535752260)*(0.166648917650934*x + 0.561353249199241)*(0.189957998488206*x + 0.500000000000000)*(0.225307983013055*x + 0.406953155944514)*(0.281618078073456*x + 0.258735930272134)*(0.583630373124159*x - 0.536208998223347)*(1.21072340120799*x - 2.18681869372076)*x + 0.00621382523136126*(-1.21072340120799*x + 3.18681869372076)*(-0.640094268046196*x + 2.15614359952927)*(-0.457901077385086*x + 1.82706474071741)*(-0.374586813068497*x + 1.67658182242300)*(-0.333009217135297*x + 1.60148402226817)*(-0.315212546742269*x + 1.56933952794137)*(0.147386558948727*x + 0.733789169358853)*(0.151163889081916*x + 0.726966524203593)*(0.159184344824013*x + 0.712479910224315)*(0.172524016099451*x + 0.688385684834676)*(0.193248420073033*x + 0.650953093723913)*(0.225307983013055*x + 0.593046844055486)*(0.276822995130888*x + 0.500000000000000)*(0.366978413358396*x + 0.337160532518476)*(1.12681040731122*x - 1.03525434507065)*x - 0.0000531711111847143*(-1.21072340120799*x - 2.18681869372076)*(-0.583630373124159*x - 0.536208998223346)*(-0.281618078073455*x + 0.258735930272134)*(-0.225307983013055*x + 0.406953155944514)*(-0.189957998488206*x + 0.500000000000000)*(-0.166648917650934*x + 0.561353249199241)*(-0.151006147525352*x + 0.602527535752260)*(-0.140687000232418*x + 0.629689190894607)*(-0.134385318986365*x + 0.646276229335223)*(-0.131391684898735*x + 0.654155955673294)*(0.426164802796190*x + 2.12173429439100)*(0.459354604630914*x + 2.20909519021762)*(0.542400639798688*x + 2.42768570977642)*(0.736417521485311*x + 2.93836934308147)*(1.35810996015672*x + 4.57476381875291)*x - 0.00621382523136129*(-1.12681040731122*x - 1.03525434507065)*(-0.366978413358396*x + 0.337160532518477)*(-0.276822995130888*x + 0.500000000000000)*(-0.225307983013055*x + 0.593046844055486)*(-0.193248420073033*x + 0.650953093723913)*(-0.172524016099451*x + 0.688385684834676)*(-0.159184344824013*x + 0.712479910224315)*(-0.151163889081916*x + 0.726966524203593)*(-0.147386558948727*x + 0.733789169358853)*(0.315212546742269*x + 1.56933952794136)*(0.333009217135297*x + 1.60148402226817)*(0.374586813068498*x + 1.67658182242300)*(0.457901077385086*x + 1.82706474071741)*(0.640094268046196*x + 2.15614359952927)*(1.21072340120799*x + 3.18681869372076)*x + 0.357603511397639*(-1.12681040731122*x + 2.03525434507065)*(-0.583630373124159*x + 1.53620899822335)*(-0.408208146683868*x + 1.37504025060978)*(-0.325590938476360*x + 1.29913588975238)*(-0.281130345572623*x + 1.25828782721288)*(-0.257044257601952*x + 1.23615879195938)*(-0.246310072378424*x + 1.22629678516450)*(0.169565718456703*x + 0.844211904976803)*(0.174584790951008*x + 0.839600644223228)*(0.185371791214117*x + 0.829690113738060)*(0.203714376147746*x + 0.812837908052741)*(0.233251068393370*x + 0.785701143262592)*(0.281618078073455*x + 0.741264069727866)*(0.366978413358396*x + 0.662839467481523)*(0.544219115175180*x + 0.500000000000000)*x + (-1.08843823035036*x + 1.00000000000000)*(-0.553645990261775*x + 1.00000000000000)*(-0.379915996976413*x + 1.00000000000000)*(-0.296869961808639*x + 1.00000000000000)*(-0.250621155988862*x + 1.00000000000000)*(-0.223422923986581*x + 1.00000000000000)*(-0.207937895417563*x + 1.00000000000000)*(-0.200856819783135*x + 1.00000000000000)*(0.200856819783135*x + 1.00000000000000)*(0.207937895417563*x + 1.00000000000000)*(0.223422923986581*x + 1.00000000000000)*(0.250621155988862*x + 1.00000000000000)*(0.296869961808639*x + 1.00000000000000)*(0.379915996976413*x + 1.00000000000000)*(0.553645990261775*x + 1.00000000000000)*(1.08843823035036*x + 1.00000000000000) - 0.357603511397640*(-0.544219115175180*x + 0.500000000000000)*(-0.366978413358396*x + 0.662839467481524)*(-0.281618078073456*x + 0.741264069727866)*(-0.233251068393370*x + 0.785701143262592)*(-0.203714376147746*x + 0.812837908052741)*(-0.185371791214117*x + 0.829690113738060)*(-0.174584790951008*x + 0.839600644223228)*(-0.169565718456703*x + 0.844211904976803)*(0.246310072378424*x + 1.22629678516450)*(0.257044257601952*x + 1.23615879195938)*(0.281130345572623*x + 1.25828782721288)*(0.325590938476360*x + 1.29913588975238)*(0.408208146683868*x + 1.37504025060978)*(0.583630373124159*x + 1.53620899822335)*(1.12681040731122*x + 2.03525434507065)*x + (1.39116348212640e-13)*(0.100428409891567*x + 0.500000000000000)*(0.102168014489779*x + 0.491339081241606)*(0.105769880927785*x + 0.473406573687743)*(0.111498170594522*x + 0.444887304723300)*(0.119801382250976*x + 0.403548346626591)*(0.131391684898735*x + 0.345844044326706)*(0.147386558948727*x + 0.266210830641147)*(0.169565718456703*x + 0.155788095023197)*(0.246310072378424*x - 0.226296785164500)*(0.315212546742269*x - 0.569339527941365)*(0.426164802796190*x - 1.12173429439100)*(0.621043694228700*x - 2.09197215658020)*(1.01154706764686*x - 4.03615993093503)*(1.98864711312200*x - 8.90081947563015)*(5.89822034704794*x - 28.3652978943719)*x Der Fehler ist: Der Fehler ist: 0.0601105640876 None Polynom bei n= 2 ist: (-0.230940107675850*x + 1.00000000000000)*(0.230940107675850*x + 1.00000000000000) - (8.84829859138229e-11)*(-0.115470053837925*x + 0.500000000000000)*x + (8.84829859138229e-11)*(0.115470053837925*x + 0.500000000000000)*x Der Fehler ist: Der Fehler ist: 1.65537028244 None Polynom bei n= 4 ist: (6.94090694647205e-6)*(-0.550552768188470*x + 2.61803398874990)*(0.129967878493163*x + 0.618033988749895)*(0.170130161670408*x + 0.500000000000000)*x - (1.40433438138665e-12)*(-0.550552768188469*x - 1.61803398874989)*(-0.129967878493163*x + 0.381966011250105)*(-0.105146222423827*x + 0.500000000000000)*x + (-0.340260323340816*x + 1.00000000000000)*(-0.210292444847653*x + 1.00000000000000)*(0.210292444847653*x + 1.00000000000000)*(0.340260323340816*x + 1.00000000000000) - (6.94090694647209e-6)*(-0.170130161670408*x + 0.500000000000000)*(-0.129967878493163*x + 0.618033988749895)*(0.550552768188469*x + 2.61803398874989)*x + (1.40433438138665e-12)*(0.105146222423827*x + 0.500000000000000)*(0.129967878493163*x + 0.381966011250105)*(0.550552768188470*x - 1.61803398874990)*x Der Fehler ist: Der Fehler ist: 1.06191869596 None Polynom bei n= 8 ist: -(2.46998334944342e-13)*(-1.68375184781447*x - 7.29085936938159)*(-0.584760880032618*x - 1.87938524157182)*(-0.311144765372083*x - 0.532088886237956)*(-0.150735449979618*x + 0.257772801031441)*(-0.122880664680917*x + 0.394930843634698)*(-0.108059442994933*x + 0.467911113762044)*(-0.101542661188575*x + 0.500000000000000)*x + (8.84829859138229e-11)*(-1.68375184781447*x + 8.29085936938159)*(0.108059442994933*x + 0.532088886237956)*(0.115470053837925*x + 0.500000000000000)*(0.132554530093763*x + 0.426022047760462)*(0.165556671665602*x + 0.283118582857949)*(0.381675557655469*x - 0.652703644666140)*(0.895905645404700*x - 2.87938524157182)*x - (8.84829859138229e-11)*(-0.895905645404700*x - 2.87938524157182)*(-0.381675557655469*x - 0.652703644666139)*(-0.165556671665602*x + 0.283118582857949)*(-0.132554530093763*x + 0.426022047760462)*(-0.115470053837925*x + 0.500000000000000)*(-0.108059442994933*x + 0.532088886237956)*(1.68375184781447*x + 8.29085936938159)*x + (9.79177286950834e-7)*(-0.895905645404700*x + 3.87938524157182)*(-0.584760880032618*x + 2.87938524157182)*(0.122880664680917*x + 0.605069156365302)*(0.132554530093763*x + 0.573977952239538)*(0.155572382686041*x + 0.500000000000000)*(0.203085322377149*x + 0.347296355333861)*(0.664965537728850*x - 1.13715804260326)*x + 0.0101590366730642*(-0.664965537728850*x + 2.13715804260326)*(-0.381675557655469*x + 1.65270364466614)*(-0.311144765372083*x + 1.53208888623796)*(0.150735449979618*x + 0.742227198968559)*(0.165556671665602*x + 0.716881417142051)*(0.203085322377149*x + 0.652703644666139)*(0.292380440016309*x + 0.500000000000000)*x - (9.79177286950834e-7)*(-0.664965537728849*x - 1.13715804260326)*(-0.203085322377149*x + 0.347296355333861)*(-0.155572382686041*x + 0.500000000000000)*(-0.132554530093763*x + 0.573977952239538)*(-0.122880664680917*x + 0.605069156365302)*(0.584760880032618*x + 2.87938524157182)*(0.895905645404700*x + 3.87938524157182)*x + (-0.584760880032617*x + 1.00000000000000)*(-0.311144765372082*x + 1.00000000000000)*(-0.230940107675850*x + 1.00000000000000)*(-0.203085322377149*x + 1.00000000000000)*(0.203085322377149*x + 1.00000000000000)*(0.230940107675850*x + 1.00000000000000)*(0.311144765372082*x + 1.00000000000000)*(0.584760880032618*x + 1.00000000000000) - 0.0101590366730642*(-0.292380440016309*x + 0.500000000000000)*(-0.203085322377149*x + 0.652703644666139)*(-0.165556671665602*x + 0.716881417142052)*(-0.150735449979618*x + 0.742227198968559)*(0.311144765372083*x + 1.53208888623796)*(0.381675557655469*x + 1.65270364466614)*(0.664965537728849*x + 2.13715804260326)*x + (2.46998334944342e-13)*(0.101542661188575*x + 0.500000000000000)*(0.108059442994933*x + 0.467911113762044)*(0.122880664680917*x + 0.394930843634698)*(0.150735449979618*x + 0.257772801031441)*(0.311144765372083*x - 0.532088886237956)*(0.584760880032618*x - 1.87938524157182)*(1.68375184781447*x - 7.29085936938159)*x Der Fehler ist: Der Fehler ist: 0.458252697981 None Polynom bei n= 16 ist: -(1.39116348212640e-13)*(-5.89822034704794*x - 28.3652978943719)*(-1.98864711312199*x - 8.90081947563013)*(-1.01154706764686*x - 4.03615993093503)*(-0.621043694228700*x - 2.09197215658020)*(-0.426164802796190*x - 1.12173429439100)*(-0.315212546742269*x - 0.569339527941365)*(-0.246310072378424*x - 0.226296785164499)*(-0.169565718456703*x + 0.155788095023197)*(-0.147386558948727*x + 0.266210830641147)*(-0.131391684898735*x + 0.345844044326706)*(-0.119801382250976*x + 0.403548346626591)*(-0.111498170594522*x + 0.444887304723300)*(-0.105769880927785*x + 0.473406573687743)*(-0.102168014489779*x + 0.491339081241606)*(-0.100428409891567*x + 0.500000000000000)*x + (8.11253701429134e-13)*(-5.89822034704794*x + 29.3652978943719)*(0.102168014489779*x + 0.508660918758394)*(0.103968947708782*x + 0.500000000000000)*(0.107701234122242*x + 0.482050956099341)*(0.113646509786701*x + 0.453459363150300)*(0.122285170857631*x + 0.411914934446805)*(0.134385318986365*x + 0.353723770664777)*(0.151163889081916*x + 0.273033475796407)*(0.174584790951008*x + 0.160399355776772)*(0.257044257601952*x - 0.236158791959385)*(0.333009217135297*x - 0.601484022268171)*(0.459354604630914*x - 1.20909519021762)*(0.694131122510105*x - 2.33816556677276)*(1.22093849031025*x - 4.87164974358555)*(3.00019418076886*x - 13.4283184878068)*x + (2.22152161612423e-11)*(-3.00019418076886*x + 14.4283184878068)*(-1.98864711312200*x + 9.90081947563015)*(0.105769880927785*x + 0.526593426312257)*(0.107701234122242*x + 0.517949043900659)*(0.111711461993291*x + 0.500000000000000)*(0.118120896028971*x + 0.471312549664485)*(0.127481187465585*x + 0.429417603212275)*(0.140687000232418*x + 0.370310809105393)*(0.159184344824013*x + 0.287520089775685)*(0.185371791214117*x + 0.170309886261939)*(0.281130345572623*x - 0.258287827212877)*(0.374586813068497*x - 0.676581822422998)*(0.542400639798687*x - 1.42768570977642)*(0.903066439136245*x - 3.04195962984748)*(2.05875556467175*x - 8.21461203683558)*x - (8.11253701429134e-13)*(-3.00019418076885*x - 13.4283184878068)*(-1.22093849031025*x - 4.87164974358555)*(-0.694131122510105*x - 2.33816556677276)*(-0.459354604630914*x - 1.20909519021762)*(-0.333009217135297*x - 0.601484022268171)*(-0.257044257601952*x - 0.236158791959385)*(-0.174584790951008*x + 0.160399355776773)*(-0.151163889081916*x + 0.273033475796407)*(-0.134385318986365*x + 0.353723770664777)*(-0.122285170857631*x + 0.411914934446805)*(-0.113646509786701*x + 0.453459363150300)*(-0.107701234122242*x + 0.482050956099341)*(-0.103968947708782*x + 0.500000000000000)*(-0.102168014489779*x + 0.508660918758394)*(5.89822034704794*x + 29.3652978943719)*x - (2.22152161612426e-11)*(-2.05875556467176*x - 8.21461203683559)*(-0.903066439136245*x - 3.04195962984749)*(-0.542400639798688*x - 1.42768570977642)*(-0.374586813068498*x - 0.676581822422998)*(-0.281130345572623*x - 0.258287827212876)*(-0.185371791214117*x + 0.170309886261940)*(-0.159184344824013*x + 0.287520089775685)*(-0.140687000232418*x + 0.370310809105393)*(-0.127481187465585*x + 0.429417603212275)*(-0.118120896028971*x + 0.471312549664485)*(-0.111711461993291*x + 0.500000000000000)*(-0.107701234122242*x + 0.517949043900659)*(-0.105769880927785*x + 0.526593426312257)*(1.98864711312199*x + 9.90081947563013)*(3.00019418076885*x + 14.4283184878068)*x + (1.91376264845534e-9)*(-2.05875556467175*x + 9.21461203683558)*(-1.22093849031025*x + 5.87164974358555)*(-1.01154706764686*x + 5.03615993093503)*(0.111498170594522*x + 0.555112695276700)*(0.113646509786701*x + 0.546540636849700)*(0.118120896028971*x + 0.528687450335515)*(0.125310577994431*x + 0.500000000000000)*(0.135896073174961*x + 0.457762962433225)*(0.151006147525352*x + 0.397472464247740)*(0.172524016099451*x + 0.311614315165324)*(0.203714376147746*x + 0.187162091947259)*(0.325590938476360*x - 0.299135889752379)*(0.457901077385086*x - 0.827064740717406)*(0.736417521485310*x - 1.93836934308147)*(1.60873111614558*x - 5.41897572372971)*x - (1.91376264845534e-9)*(-1.60873111614558*x - 5.41897572372971)*(-0.736417521485311*x - 1.93836934308147)*(-0.457901077385086*x - 0.827064740717405)*(-0.325590938476360*x - 0.299135889752379)*(-0.203714376147746*x + 0.187162091947259)*(-0.172524016099451*x + 0.311614315165324)*(-0.151006147525352*x + 0.397472464247740)*(-0.135896073174961*x + 0.457762962433225)*(-0.125310577994431*x + 0.500000000000000)*(-0.118120896028971*x + 0.528687450335515)*(-0.113646509786701*x + 0.546540636849700)*(-0.111498170594522*x + 0.555112695276700)*(1.01154706764686*x + 5.03615993093503)*(1.22093849031025*x + 5.87164974358555)*(2.05875556467176*x + 9.21461203683559)*x + (3.07774848688181e-7)*(-1.60873111614558*x + 6.41897572372971)*(-0.903066439136245*x + 4.04195962984748)*(-0.694131122510105*x + 3.33816556677276)*(-0.621043694228700*x + 3.09197215658020)*(0.119801382250976*x + 0.596451653373409)*(0.122285170857631*x + 0.588085065553195)*(0.127481187465585*x + 0.570582396787725)*(0.135896073174961*x + 0.542237037566775)*(0.148434980904320*x + 0.500000000000000)*(0.166648917650934*x + 0.438646750800759)*(0.193248420073033*x + 0.349046906276087)*(0.233251068393370*x + 0.214298856737408)*(0.408208146683868*x - 0.375040250609783)*(0.640094268046196*x - 1.15614359952927)*(1.35810996015672*x - 3.57476381875291)*x - (3.07774848688181e-7)*(-1.35810996015672*x - 3.57476381875291)*(-0.640094268046196*x - 1.15614359952927)*(-0.408208146683868*x - 0.375040250609783)*(-0.233251068393370*x + 0.214298856737408)*(-0.193248420073033*x + 0.349046906276087)*(-0.166648917650934*x + 0.438646750800758)*(-0.148434980904320*x + 0.500000000000000)*(-0.135896073174961*x + 0.542237037566775)*(-0.127481187465585*x + 0.570582396787725)*(-0.122285170857631*x + 0.588085065553195)*(-0.119801382250976*x + 0.596451653373409)*(0.621043694228700*x + 3.09197215658020)*(0.694131122510105*x + 3.33816556677276)*(0.903066439136245*x + 4.04195962984749)*(1.60873111614558*x + 6.41897572372971)*x + 0.0000531711111847144*(-1.35810996015672*x + 4.57476381875291)*(-0.736417521485310*x + 2.93836934308147)*(-0.542400639798687*x + 2.42768570977642)*(-0.459354604630914*x + 2.20909519021762)*(-0.426164802796190*x + 2.12173429439100)*(0.131391684898735*x + 0.654155955673294)*(0.134385318986365*x + 0.646276229335223)*(0.140687000232418*x + 0.629689190894607)*(0.151006147525352*x + 0.602527535752260)*(0.166648917650934*x + 0.561353249199241)*(0.189957998488206*x + 0.500000000000000)*(0.225307983013055*x + 0.406953155944514)*(0.281618078073456*x + 0.258735930272134)*(0.583630373124159*x - 0.536208998223347)*(1.21072340120799*x - 2.18681869372076)*x + 0.00621382523136126*(-1.21072340120799*x + 3.18681869372076)*(-0.640094268046196*x + 2.15614359952927)*(-0.457901077385086*x + 1.82706474071741)*(-0.374586813068497*x + 1.67658182242300)*(-0.333009217135297*x + 1.60148402226817)*(-0.315212546742269*x + 1.56933952794137)*(0.147386558948727*x + 0.733789169358853)*(0.151163889081916*x + 0.726966524203593)*(0.159184344824013*x + 0.712479910224315)*(0.172524016099451*x + 0.688385684834676)*(0.193248420073033*x + 0.650953093723913)*(0.225307983013055*x + 0.593046844055486)*(0.276822995130888*x + 0.500000000000000)*(0.366978413358396*x + 0.337160532518476)*(1.12681040731122*x - 1.03525434507065)*x - 0.0000531711111847143*(-1.21072340120799*x - 2.18681869372076)*(-0.583630373124159*x - 0.536208998223346)*(-0.281618078073455*x + 0.258735930272134)*(-0.225307983013055*x + 0.406953155944514)*(-0.189957998488206*x + 0.500000000000000)*(-0.166648917650934*x + 0.561353249199241)*(-0.151006147525352*x + 0.602527535752260)*(-0.140687000232418*x + 0.629689190894607)*(-0.134385318986365*x + 0.646276229335223)*(-0.131391684898735*x + 0.654155955673294)*(0.426164802796190*x + 2.12173429439100)*(0.459354604630914*x + 2.20909519021762)*(0.542400639798688*x + 2.42768570977642)*(0.736417521485311*x + 2.93836934308147)*(1.35810996015672*x + 4.57476381875291)*x - 0.00621382523136129*(-1.12681040731122*x - 1.03525434507065)*(-0.366978413358396*x + 0.337160532518477)*(-0.276822995130888*x + 0.500000000000000)*(-0.225307983013055*x + 0.593046844055486)*(-0.193248420073033*x + 0.650953093723913)*(-0.172524016099451*x + 0.688385684834676)*(-0.159184344824013*x + 0.712479910224315)*(-0.151163889081916*x + 0.726966524203593)*(-0.147386558948727*x + 0.733789169358853)*(0.315212546742269*x + 1.56933952794136)*(0.333009217135297*x + 1.60148402226817)*(0.374586813068498*x + 1.67658182242300)*(0.457901077385086*x + 1.82706474071741)*(0.640094268046196*x + 2.15614359952927)*(1.21072340120799*x + 3.18681869372076)*x + 0.357603511397639*(-1.12681040731122*x + 2.03525434507065)*(-0.583630373124159*x + 1.53620899822335)*(-0.408208146683868*x + 1.37504025060978)*(-0.325590938476360*x + 1.29913588975238)*(-0.281130345572623*x + 1.25828782721288)*(-0.257044257601952*x + 1.23615879195938)*(-0.246310072378424*x + 1.22629678516450)*(0.169565718456703*x + 0.844211904976803)*(0.174584790951008*x + 0.839600644223228)*(0.185371791214117*x + 0.829690113738060)*(0.203714376147746*x + 0.812837908052741)*(0.233251068393370*x + 0.785701143262592)*(0.281618078073455*x + 0.741264069727866)*(0.366978413358396*x + 0.662839467481523)*(0.544219115175180*x + 0.500000000000000)*x + (-1.08843823035036*x + 1.00000000000000)*(-0.553645990261775*x + 1.00000000000000)*(-0.379915996976413*x + 1.00000000000000)*(-0.296869961808639*x + 1.00000000000000)*(-0.250621155988862*x + 1.00000000000000)*(-0.223422923986581*x + 1.00000000000000)*(-0.207937895417563*x + 1.00000000000000)*(-0.200856819783135*x + 1.00000000000000)*(0.200856819783135*x + 1.00000000000000)*(0.207937895417563*x + 1.00000000000000)*(0.223422923986581*x + 1.00000000000000)*(0.250621155988862*x + 1.00000000000000)*(0.296869961808639*x + 1.00000000000000)*(0.379915996976413*x + 1.00000000000000)*(0.553645990261775*x + 1.00000000000000)*(1.08843823035036*x + 1.00000000000000) - 0.357603511397640*(-0.544219115175180*x + 0.500000000000000)*(-0.366978413358396*x + 0.662839467481524)*(-0.281618078073456*x + 0.741264069727866)*(-0.233251068393370*x + 0.785701143262592)*(-0.203714376147746*x + 0.812837908052741)*(-0.185371791214117*x + 0.829690113738060)*(-0.174584790951008*x + 0.839600644223228)*(-0.169565718456703*x + 0.844211904976803)*(0.246310072378424*x + 1.22629678516450)*(0.257044257601952*x + 1.23615879195938)*(0.281130345572623*x + 1.25828782721288)*(0.325590938476360*x + 1.29913588975238)*(0.408208146683868*x + 1.37504025060978)*(0.583630373124159*x + 1.53620899822335)*(1.12681040731122*x + 2.03525434507065)*x + (1.39116348212640e-13)*(0.100428409891567*x + 0.500000000000000)*(0.102168014489779*x + 0.491339081241606)*(0.105769880927785*x + 0.473406573687743)*(0.111498170594522*x + 0.444887304723300)*(0.119801382250976*x + 0.403548346626591)*(0.131391684898735*x + 0.345844044326706)*(0.147386558948727*x + 0.266210830641147)*(0.169565718456703*x + 0.155788095023197)*(0.246310072378424*x - 0.226296785164500)*(0.315212546742269*x - 0.569339527941365)*(0.426164802796190*x - 1.12173429439100)*(0.621043694228700*x - 2.09197215658020)*(1.01154706764686*x - 4.03615993093503)*(1.98864711312200*x - 8.90081947563015)*(5.89822034704794*x - 28.3652978943719)*x Der Fehler ist: Der Fehler ist: 0.0601105640876 None |
#Mit tschebyscheff wird fehler immer kleiner
PnTschebMit2Stst=plot(pntscheb(f,2),-5,5,color='yellow')
PnTschebMit8Stst=plot(pntscheb(f,8),-5,5,color='red')
PnTschebMit16Stst=plot(pntscheb(f,16),-5,5,color='black')
PnTschebMit32Stst=plot(pntscheb(f,32),-5,5,color='green')
PnTschebMit64Stst=plot(pntscheb(f,64),-5,5,color='purple')
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show(Funktion1+PnTschebMit2Stst+PnTschebMit8Stst+PnTschebMit16Stst+PnTschebMit32Stst+PnTschebMit64Stst)
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#############################################################################################################################################
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# Zweite Funktion sin(x)
def g(x):
return sin(x)
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#Gleichverteilte Stützstellen neu definieren im intervall [0,2]
def stst2(x,n):
return 0+(2)*x/n
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#definiere die Li mit den Neuen Stützstellen neu
def Li2(j,n):
sum=1;
for i in range(n+1):
if(i != j):
sum*=(x-stst2(i,n))/(stst2(j,n)-stst2(i,n))
return sum
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|
#definiere Interpolationspolynom mit gleichverteilten Stützstellen neu
def pn2(f,n):
poly=0;
for j in range(n+1):
poly+= f(stst2(j,n))*Li2(j,n)
return poly
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|
#############################################################################################################################################
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#definiere Tschebyscheff Nst neu für n+1 Tschebyscheff-polynom und transformiere sie auf Intervall [0,2]
def tscheb2(x,n):
return ((1/2)*((cos((2*x+1)/(n+1)*pi/2))*2+2)).n()
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|
#definiere Li mi Tschebyscheff NST neu
def Litscheb2(j,n):
sum=1;
for i in range(n+1):
if(i != j):
sum*=(x-tscheb2(i,n))/(tscheb2(j,n)-tscheb2(i,n))
return sum
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|
#definiere Interpolationspolynom mit Tschebyscheff NST neu
def pntscheb2(f,n):
poly=0;
for j in range(n+1):
poly+= f(tscheb2(j,n))*Litscheb2(j,n)
return poly
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#############################################################################################################################################
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#definiere Fehler für Gleichverteilte Stützstellen neu
def fehler2(n):
poly= pn2(g,n)
print 'Der Fehler ist:', sqrt(integral((sin(x) - poly)^2,x,0,2)).n()
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#Ausgabe für gleichverteilte Stützstellen neu
for i in range(1,5):
print 'Polynom bei n=',2^i,'ist:', view(factor(pn2(g,2^i)))
print 'Der Fehler ist:', fehler2(2^i)
Polynom bei n= 2 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, {\left(2 \, x \sin\left(1\right) - x \sin\left(2\right) - 4 \, \sin\left(1\right) + \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 0.0337223120286097 None Polynom bei n= 4 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{6} \, {\left(16 \, x^{3} \sin\left(\frac{1}{2}\right) - 24 \, x^{3} \sin\left(1\right) + 16 \, x^{3} \sin\left(\frac{3}{2}\right) - 4 \, x^{3} \sin\left(2\right) - 72 \, x^{2} \sin\left(\frac{1}{2}\right) + 96 \, x^{2} \sin\left(1\right) - 56 \, x^{2} \sin\left(\frac{3}{2}\right) + 12 \, x^{2} \sin\left(2\right) + 104 \, x \sin\left(\frac{1}{2}\right) - 114 \, x \sin\left(1\right) + 56 \, x \sin\left(\frac{3}{2}\right) - 11 \, x \sin\left(2\right) - 48 \, \sin\left(\frac{1}{2}\right) + 36 \, \sin\left(1\right) - 16 \, \sin\left(\frac{3}{2}\right) + 3 \, \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 0.000373252230370591 None Polynom bei n= 8 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{630} \, {\left(8192 \, x^{7} \sin\left(\frac{1}{4}\right) - 28672 \, x^{7} \sin\left(\frac{1}{2}\right) + 57344 \, x^{7} \sin\left(\frac{3}{4}\right) - 71680 \, x^{7} \sin\left(1\right) + 57344 \, x^{7} \sin\left(\frac{5}{4}\right) - 28672 \, x^{7} \sin\left(\frac{3}{2}\right) + 8192 \, x^{7} \sin\left(\frac{7}{4}\right) - 1024 \, x^{7} \sin\left(2\right) - 71680 \, x^{6} \sin\left(\frac{1}{4}\right) + 243712 \, x^{6} \sin\left(\frac{1}{2}\right) - 473088 \, x^{6} \sin\left(\frac{3}{4}\right) + 573440 \, x^{6} \sin\left(1\right) - 444416 \, x^{6} \sin\left(\frac{5}{4}\right) + 215040 \, x^{6} \sin\left(\frac{3}{2}\right) - 59392 \, x^{6} \sin\left(\frac{7}{4}\right) + 7168 \, x^{6} \sin\left(2\right) + 261632 \, x^{5} \sin\left(\frac{1}{4}\right) - 856576 \, x^{5} \sin\left(\frac{1}{2}\right) + 1602048 \, x^{5} \sin\left(\frac{3}{4}\right) - 1872640 \, x^{5} \sin\left(1\right) + 1401344 \, x^{5} \sin\left(\frac{5}{4}\right) - 655872 \, x^{5} \sin\left(\frac{3}{2}\right) + 175616 \, x^{5} \sin\left(\frac{7}{4}\right) - 20608 \, x^{5} \sin\left(2\right) - 515200 \, x^{4} \sin\left(\frac{1}{4}\right) + 1603840 \, x^{4} \sin\left(\frac{1}{2}\right) - 2862720 \, x^{4} \sin\left(\frac{3}{4}\right) + 3207680 \, x^{4} \sin\left(1\right) - 2312576 \, x^{4} \sin\left(\frac{5}{4}\right) + 1048320 \, x^{4} \sin\left(\frac{3}{2}\right) - 273280 \, x^{4} \sin\left(\frac{7}{4}\right) + 31360 \, x^{4} \sin\left(2\right) + 589568 \, x^{3} \sin\left(\frac{1}{4}\right) - 1712368 \, x^{3} \sin\left(\frac{1}{2}\right) + 2881536 \, x^{3} \sin\left(\frac{3}{4}\right) - 3078040 \, x^{3} \sin\left(1\right) + 2137856 \, x^{3} \sin\left(\frac{5}{4}\right) - 941808 \, x^{3} \sin\left(\frac{3}{2}\right) + 240128 \, x^{3} \sin\left(\frac{7}{4}\right) - 27076 \, x^{3} \sin\left(2\right) - 390880 \, x^{2} \sin\left(\frac{1}{4}\right) + 1027768 \, x^{2} \sin\left(\frac{1}{2}\right) - 1606752 \, x^{2} \sin\left(\frac{3}{4}\right) + 1631840 \, x^{2} \sin\left(1\right) - 1095584 \, x^{2} \sin\left(\frac{5}{4}\right) + 471240 \, x^{2} \sin\left(\frac{3}{2}\right) - 118048 \, x^{2} \sin\left(\frac{7}{4}\right) + 13132 \, x^{2} \sin\left(2\right) + 138528 \, x \sin\left(\frac{1}{4}\right) - 312984 \, x \sin\left(\frac{1}{2}\right) + 448672 \, x \sin\left(\frac{3}{4}\right) - 435330 \, x \sin\left(1\right) + 284256 \, x \sin\left(\frac{5}{4}\right) - 120008 \, x \sin\left(\frac{3}{2}\right) + 29664 \, x \sin\left(\frac{7}{4}\right) - 3267 \, x \sin\left(2\right) - 20160 \, \sin\left(\frac{1}{4}\right) + 35280 \, \sin\left(\frac{1}{2}\right) - 47040 \, \sin\left(\frac{3}{4}\right) + 44100 \, \sin\left(1\right) - 28224 \, \sin\left(\frac{5}{4}\right) + 11760 \, \sin\left(\frac{3}{2}\right) - 2880 \, \sin\left(\frac{7}{4}\right) + 315 \, \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 0.0000245789030322370 None Polynom bei n= 16 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{1277025750} \, {\left(274877906944 \, x^{15} \sin\left(\frac{1}{8}\right) - 2061584302080 \, x^{15} \sin\left(\frac{1}{4}\right) + 9620726743040 \, x^{15} \sin\left(\frac{3}{8}\right) - 31267361914880 \, x^{15} \sin\left(\frac{1}{2}\right) + 75041668595712 \, x^{15} \sin\left(\frac{5}{8}\right) - 137576392425472 \, x^{15} \sin\left(\frac{3}{4}\right) + 196537703464960 \, x^{15} \sin\left(\frac{7}{8}\right) - 221104916398080 \, x^{15} \sin\left(1\right) + 196537703464960 \, x^{15} \sin\left(\frac{9}{8}\right) - 137576392425472 \, x^{15} \sin\left(\frac{5}{4}\right) + 75041668595712 \, x^{15} \sin\left(\frac{11}{8}\right) - 31267361914880 \, x^{15} \sin\left(\frac{3}{2}\right) + 9620726743040 \, x^{15} \sin\left(\frac{13}{8}\right) - 2061584302080 \, x^{15} \sin\left(\frac{7}{4}\right) + 274877906944 \, x^{15} \sin\left(\frac{15}{8}\right) - 17179869184 \, x^{15} \sin\left(2\right) - 4638564679680 \, x^{14} \sin\left(\frac{1}{8}\right) + 34531537059840 \, x^{14} \sin\left(\frac{1}{4}\right) - 159944582103040 \, x^{14} \sin\left(\frac{3}{8}\right) + 515911471595520 \, x^{14} \sin\left(\frac{1}{2}\right) - 1228807323254784 \, x^{14} \sin\left(\frac{5}{8}\right) + 2235616376913920 \, x^{14} \sin\left(\frac{3}{4}\right) - 3169170468372480 \, x^{14} \sin\left(\frac{7}{8}\right) + 3537678662369280 \, x^{14} \sin\left(1\right) - 3120036042506240 \, x^{14} \sin\left(\frac{9}{8}\right) + 2166828180701184 \, x^{14} \sin\left(\frac{5}{4}\right) - 1172526071808000 \, x^{14} \sin\left(\frac{11}{8}\right) + 484644109680640 \, x^{14} \sin\left(\frac{3}{2}\right) - 147918673674240 \, x^{14} \sin\left(\frac{13}{8}\right) + 31439160606720 \, x^{14} \sin\left(\frac{7}{4}\right) - 4157528342528 \, x^{14} \sin\left(\frac{15}{8}\right) + 257698037760 \, x^{14} \sin\left(2\right) + 35927401431040 \, x^{13} \sin\left(\frac{1}{8}\right) - 265171280855040 \, x^{13} \sin\left(\frac{1}{4}\right) + 1217773552271360 \, x^{13} \sin\left(\frac{3}{8}\right) - 3894740768522240 \, x^{13} \sin\left(\frac{1}{2}\right) + 9198467033333760 \, x^{13} \sin\left(\frac{5}{8}\right) - 16595152336322560 \, x^{13} \sin\left(\frac{3}{4}\right) + 23329639581614080 \, x^{13} \sin\left(\frac{7}{8}\right) - 25827818046750720 \, x^{13} \sin\left(1\right) + 22592623193620480 \, x^{13} \sin\left(\frac{9}{8}\right) - 15563329393131520 \, x^{13} \sin\left(\frac{5}{4}\right) + 8354248261632000 \, x^{13} \sin\left(\frac{11}{8}\right) - 3425730339799040 \, x^{13} \sin\left(\frac{3}{2}\right) + 1037384925839360 \, x^{13} \sin\left(\frac{13}{8}\right) - 218785634058240 \, x^{13} \sin\left(\frac{7}{4}\right) + 28711856373760 \, x^{13} \sin\left(\frac{15}{8}\right) - 1766305300480 \, x^{13} \sin\left(2\right) - 169283451617280 \, x^{12} \sin\left(\frac{1}{8}\right) + 1237015005757440 \, x^{12} \sin\left(\frac{1}{4}\right) - 5625438105763840 \, x^{12} \sin\left(\frac{3}{8}\right) + 17819464976302080 \, x^{12} \sin\left(\frac{1}{2}\right) - 41691362969518080 \, x^{12} \sin\left(\frac{5}{8}\right) + 74527711334236160 \, x^{12} \sin\left(\frac{3}{4}\right) - 103835244775342080 \, x^{12} \sin\left(\frac{7}{8}\right) + 113951946288660480 \, x^{12} \sin\left(1\right) - 98831978316431360 \, x^{12} \sin\left(\frac{9}{8}\right) + 67519913845063680 \, x^{12} \sin\left(\frac{5}{4}\right) - 35953313505607680 \, x^{12} \sin\left(\frac{11}{8}\right) + 14628239850864640 \, x^{12} \sin\left(\frac{3}{2}\right) - 4396352683376640 \, x^{12} \sin\left(\frac{13}{8}\right) + 920432966369280 \, x^{12} \sin\left(\frac{7}{4}\right) - 119939646095360 \, x^{12} \sin\left(\frac{15}{8}\right) + 7328287948800 \, x^{12} \sin\left(2\right) + 542152849358848 \, x^{11} \sin\left(\frac{1}{8}\right) - 3915595854643200 \, x^{11} \sin\left(\frac{1}{4}\right) + 17606425538723840 \, x^{11} \sin\left(\frac{3}{8}\right) - 55167153204101120 \, x^{11} \sin\left(\frac{1}{2}\right) + 127727423805456384 \, x^{11} \sin\left(\frac{5}{8}\right) - 226042513545232384 \, x^{11} \sin\left(\frac{3}{4}\right) + 311913156601446400 \, x^{11} \sin\left(\frac{7}{8}\right) - 339163173963694080 \, x^{11} \sin\left(1\right) + 291583020173885440 \, x^{11} \sin\left(\frac{9}{8}\right) - 197538404739579904 \, x^{11} \sin\left(\frac{5}{4}\right) + 104348719591194624 \, x^{11} \sin\left(\frac{11}{8}\right) - 42134525915955200 \, x^{11} \sin\left(\frac{3}{2}\right) + 12571891717898240 \, x^{11} \sin\left(\frac{13}{8}\right) - 2614091914936320 \, x^{11} \sin\left(\frac{7}{4}\right) + 338426444382208 \, x^{11} \sin\left(\frac{15}{8}\right) - 20550504153088 \, x^{11} \sin\left(2\right) - 1248843320524800 \, x^{10} \sin\left(\frac{1}{8}\right) + 8895694236549120 \, x^{10} \sin\left(\frac{1}{4}\right) - 39479025357291520 \, x^{10} \sin\left(\frac{3}{8}\right) + 122181086934466560 \, x^{10} \sin\left(\frac{1}{2}\right) - 279605552609230848 \, x^{10} \sin\left(\frac{5}{8}\right) + 489432634401751040 \, x^{10} \sin\left(\frac{3}{4}\right) - 668453873060413440 \, x^{10} \sin\left(\frac{7}{8}\right) + 719886946758819840 \, x^{10} \sin\left(1\right) - 613346987391057920 \, x^{10} \sin\left(\frac{9}{8}\right) + 412041513636200448 \, x^{10} \sin\left(\frac{5}{4}\right) - 215955703049748480 \, x^{10} \sin\left(\frac{11}{8}\right) + 86562874662584320 \, x^{10} \sin\left(\frac{3}{2}\right) - 25652110892728320 \, x^{10} \sin\left(\frac{13}{8}\right) + 5299932349071360 \, x^{10} \sin\left(\frac{7}{4}\right) - 682062843478016 \, x^{10} \sin\left(\frac{15}{8}\right) + 41187268362240 \, x^{10} \sin\left(2\right) + 2135066091192320 \, x^{9} \sin\left(\frac{1}{8}\right) - 14959862737797120 \, x^{9} \sin\left(\frac{1}{4}\right) + 65386368210042880 \, x^{9} \sin\left(\frac{3}{8}\right) - 199530215369605120 \, x^{9} \sin\left(\frac{1}{2}\right) + 450736350827642880 \, x^{9} \sin\left(\frac{5}{8}\right) - 779656863080775680 \, x^{9} \sin\left(\frac{3}{4}\right) + 1053290488046551040 \, x^{9} \sin\left(\frac{7}{8}\right) - 1123074133587394560 \, x^{9} \sin\left(1\right) + 948172266159472640 \, x^{9} \sin\left(\frac{9}{8}\right) - 631679446836838400 \, x^{9} \sin\left(\frac{5}{4}\right) + 328550729515008000 \, x^{9} \sin\left(\frac{11}{8}\right) - 130776446842961920 \, x^{9} \sin\left(\frac{3}{2}\right) + 38506322518343680 \, x^{9} \sin\left(\frac{13}{8}\right) - 7908904686059520 \, x^{9} \sin\left(\frac{7}{4}\right) + 1012303674736640 \, x^{9} \sin\left(\frac{15}{8}\right) - 60823682416640 \, x^{9} \sin\left(2\right) - 2755264793149440 \, x^{8} \sin\left(\frac{1}{8}\right) + 18926144724664320 \, x^{8} \sin\left(\frac{1}{4}\right) - 81255293830430720 \, x^{8} \sin\left(\frac{3}{8}\right) + 244004233520087040 \, x^{8} \sin\left(\frac{1}{2}\right) - 543336199624458240 \, x^{8} \sin\left(\frac{5}{8}\right) + 927842453990932480 \, x^{8} \sin\left(\frac{3}{4}\right) - 1239206681961431040 \, x^{8} \sin\left(\frac{7}{8}\right) + 1307866207790039040 \, x^{8} \sin\left(1\right) - 1094142059572756480 \, x^{8} \sin\left(\frac{9}{8}\right) + 722985792755466240 \, x^{8} \sin\left(\frac{5}{4}\right) - 373289165808599040 \, x^{8} \sin\left(\frac{11}{8}\right) + 147604670940446720 \, x^{8} \sin\left(\frac{3}{2}\right) - 43202407816888320 \, x^{8} \sin\left(\frac{13}{8}\right) + 8825527208509440 \, x^{8} \sin\left(\frac{7}{4}\right) - 1124078664417280 \, x^{8} \sin\left(\frac{15}{8}\right) + 67236888576000 \, x^{8} \sin\left(2\right) + 2702248761884672 \, x^{7} \sin\left(\frac{1}{8}\right) - 18118390276546560 \, x^{7} \sin\left(\frac{1}{4}\right) + 76162254949580800 \, x^{7} \sin\left(\frac{3}{8}\right) - 224555101181931520 \, x^{7} \sin\left(\frac{1}{2}\right) + 492152198295453696 \, x^{7} \sin\left(\frac{5}{8}\right) - 828969918451490816 \, x^{7} \sin\left(\frac{3}{4}\right) + 1094053808919019520 \, x^{7} \sin\left(\frac{7}{8}\right) - 1142788404799641600 \, x^{7} \sin\left(1\right) + 947449838615920640 \, x^{7} \sin\left(\frac{9}{8}\right) - 621119518000357376 \, x^{7} \sin\left(\frac{5}{4}\right) + 318464720073916416 \, x^{7} \sin\left(\frac{11}{8}\right) - 125150211531304960 \, x^{7} \sin\left(\frac{3}{2}\right) + 36429077433548800 \, x^{7} \sin\left(\frac{13}{8}\right) - 7405253842821120 \, x^{7} \sin\left(\frac{7}{4}\right) + 939009365245952 \, x^{7} \sin\left(\frac{15}{8}\right) - 55942276662272 \, x^{7} \sin\left(2\right) - 2011072733429760 \, x^{6} \sin\left(\frac{1}{8}\right) + 13086806145853440 \, x^{6} \sin\left(\frac{1}{4}\right) - 53649038397194240 \, x^{6} \sin\left(\frac{3}{8}\right) + 154904572419717120 \, x^{6} \sin\left(\frac{1}{2}\right) - 333641971290980352 \, x^{6} \sin\left(\frac{5}{8}\right) + 553873902408386560 \, x^{6} \sin\left(\frac{3}{4}\right) - 722133404691578880 \, x^{6} \sin\left(\frac{7}{8}\right) + 746570893633044480 \, x^{6} \sin\left(1\right) - 613549419052810240 \, x^{6} \sin\left(\frac{9}{8}\right) + 399201943746557952 \, x^{6} \sin\left(\frac{5}{4}\right) - 203348105124003840 \, x^{6} \sin\left(\frac{11}{8}\right) + 79456805713725440 \, x^{6} \sin\left(\frac{3}{2}\right) - 23012633173770240 \, x^{6} \sin\left(\frac{13}{8}\right) + 4657209490053120 \, x^{6} \sin\left(\frac{7}{4}\right) - 588211268829184 \, x^{6} \sin\left(\frac{15}{8}\right) + 34918810967040 \, x^{6} \sin\left(2\right) + 1124493918679040 \, x^{5} \sin\left(\frac{1}{8}\right) - 7047383541219840 \, x^{5} \sin\left(\frac{1}{4}\right) + 28037340963573760 \, x^{5} \sin\left(\frac{3}{8}\right) - 79053837468336640 \, x^{5} \sin\left(\frac{1}{2}\right) + 167088464770805760 \, x^{5} \sin\left(\frac{5}{8}\right) - 273221517377768960 \, x^{5} \sin\left(\frac{3}{4}\right) + 351886048300666880 \, x^{5} \sin\left(\frac{7}{8}\right) - 360150980948478720 \, x^{5} \sin\left(1\right) + 293509680971386880 \, x^{5} \sin\left(\frac{9}{8}\right) - 189624514500861440 \, x^{5} \sin\left(\frac{5}{4}\right) + 96011052282163200 \, x^{5} \sin\left(\frac{11}{8}\right) - 37320915107607040 \, x^{5} \sin\left(\frac{3}{2}\right) + 10760201455144960 \, x^{5} \sin\left(\frac{13}{8}\right) - 2168968470090240 \, x^{5} \sin\left(\frac{7}{4}\right) + 272981881303040 \, x^{5} \sin\left(\frac{15}{8}\right) - 16154753713280 \, x^{5} \sin\left(2\right) - 463008406049280 \, x^{4} \sin\left(\frac{1}{8}\right) + 2764930208826240 \, x^{4} \sin\left(\frac{1}{4}\right) - 10610952244605440 \, x^{4} \sin\left(\frac{3}{8}\right) + 29129185360154880 \, x^{4} \sin\left(\frac{1}{2}\right) - 60344359344622080 \, x^{4} \sin\left(\frac{5}{8}\right) + 97170719981695360 \, x^{4} \sin\left(\frac{3}{4}\right) - 123652362044090880 \, x^{4} \sin\left(\frac{7}{8}\right) + 125345755147092480 \, x^{4} \sin\left(1\right) - 101354263214364160 \, x^{4} \sin\left(\frac{9}{8}\right) + 65056214888945280 \, x^{4} \sin\left(\frac{5}{4}\right) - 32759452938401280 \, x^{4} \sin\left(\frac{11}{8}\right) + 12674731432912640 \, x^{4} \sin\left(\frac{3}{2}\right) - 3639627741335040 \, x^{4} \sin\left(\frac{13}{8}\right) + 731081271473280 \, x^{4} \sin\left(\frac{7}{4}\right) - 91729118440960 \, x^{4} \sin\left(\frac{15}{8}\right) + 5413626691200 \, x^{4} \sin\left(2\right) + 135587986177536 \, x^{3} \sin\left(\frac{1}{8}\right) - 759747724796160 \, x^{3} \sin\left(\frac{1}{4}\right) + 2792134200952320 \, x^{3} \sin\left(\frac{3}{8}\right) - 7441941521130480 \, x^{3} \sin\left(\frac{1}{2}\right) + 15100457492510208 \, x^{3} \sin\left(\frac{5}{8}\right) - 23950710499043328 \, x^{3} \sin\left(\frac{3}{4}\right) + 30130969619013120 \, x^{3} \sin\left(\frac{7}{8}\right) - 30271879561449240 \, x^{3} \sin\left(1\right) + 24303240291432960 \, x^{3} \sin\left(\frac{9}{8}\right) - 15508481874133248 \, x^{3} \sin\left(\frac{5}{4}\right) + 7771434292597248 \, x^{3} \sin\left(\frac{11}{8}\right) - 2994437051838960 \, x^{3} \sin\left(\frac{3}{2}\right) + 856846213009920 \, x^{3} \sin\left(\frac{13}{8}\right) - 171588051924480 \, x^{3} \sin\left(\frac{7}{4}\right) + 21471939856896 \, x^{3} \sin\left(\frac{15}{8}\right) - 1264248925956 \, x^{3} \sin\left(2\right) - 26590376165760 \, x^{2} \sin\left(\frac{1}{8}\right) + 136604627085600 \, x^{2} \sin\left(\frac{1}{4}\right) - 476810279971200 \, x^{2} \sin\left(\frac{3}{8}\right) + 1231576206751800 \, x^{2} \sin\left(\frac{1}{2}\right) - 2448326788742016 \, x^{2} \sin\left(\frac{5}{8}\right) + 3828173781912480 \, x^{2} \sin\left(\frac{3}{4}\right) - 4765696806499200 \, x^{2} \sin\left(\frac{7}{8}\right) + 4749702564578400 \, x^{2} \sin\left(1\right) - 3789149895273600 \, x^{2} \sin\left(\frac{9}{8}\right) + 2405604313528416 \, x^{2} \sin\left(\frac{5}{4}\right) - 1200390569239680 \, x^{2} \sin\left(\frac{11}{8}\right) + 460891389558600 \, x^{2} \sin\left(\frac{3}{2}\right) - 131485509187200 \, x^{2} \sin\left(\frac{13}{8}\right) + 26262467416800 \, x^{2} \sin\left(\frac{7}{4}\right) - 3278987206272 \, x^{2} \sin\left(\frac{15}{8}\right) + 192681800460 \, x^{2} \sin\left(2\right) + 3113218281600 \, x \sin\left(\frac{1}{8}\right) - 14126457996000 \, x \sin\left(\frac{1}{4}\right) + 46491680592000 \, x \sin\left(\frac{3}{8}\right) - 116422387263000 \, x \sin\left(\frac{1}{2}\right) + 227100934569600 \, x \sin\left(\frac{5}{8}\right) - 350595822376800 \, x \sin\left(\frac{3}{4}\right) + 432481235472000 \, x \sin\left(\frac{7}{8}\right) - 428071619225250 \, x \sin\left(1\right) + 339672308976000 \, x \sin\left(\frac{9}{8}\right) - 214720766900640 \, x \sin\left(\frac{5}{4}\right) + 106768144828800 \, x \sin\left(\frac{11}{8}\right) - 40873406301000 \, x \sin\left(\frac{3}{2}\right) + 11631583152000 \, x \sin\left(\frac{13}{8}\right) - 2318296788000 \, x \sin\left(\frac{7}{4}\right) + 288914290560 \, x \sin\left(\frac{15}{8}\right) - 16949855475 \, x \sin\left(2\right) - 163459296000 \, \sin\left(\frac{1}{8}\right) + 612972360000 \, \sin\left(\frac{1}{4}\right) - 1907025120000 \, \sin\left(\frac{3}{8}\right) + 4648373730000 \, \sin\left(\frac{1}{2}\right) - 8924877561600 \, \sin\left(\frac{5}{8}\right) + 13635229608000 \, \sin\left(\frac{3}{4}\right) - 16696199520000 \, \sin\left(\frac{7}{8}\right) + 16435321402500 \, \sin\left(1\right) - 12985932960000 \, \sin\left(\frac{9}{8}\right) + 8181137764800 \, \sin\left(\frac{5}{4}\right) - 4056762528000 \, \sin\left(\frac{11}{8}\right) + 1549457910000 \, \sin\left(\frac{3}{2}\right) - 440082720000 \, \sin\left(\frac{13}{8}\right) + 87567480000 \, \sin\left(\frac{7}{4}\right) - 10897286400 \, \sin\left(\frac{15}{8}\right) + 638512875 \, \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 2.19263792655727e-15 + 35.8084947935008*I None Polynom bei n= 2 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, {\left(2 \, x \sin\left(1\right) - x \sin\left(2\right) - 4 \, \sin\left(1\right) + \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 0.0337223120286097 None Polynom bei n= 4 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{6} \, {\left(16 \, x^{3} \sin\left(\frac{1}{2}\right) - 24 \, x^{3} \sin\left(1\right) + 16 \, x^{3} \sin\left(\frac{3}{2}\right) - 4 \, x^{3} \sin\left(2\right) - 72 \, x^{2} \sin\left(\frac{1}{2}\right) + 96 \, x^{2} \sin\left(1\right) - 56 \, x^{2} \sin\left(\frac{3}{2}\right) + 12 \, x^{2} \sin\left(2\right) + 104 \, x \sin\left(\frac{1}{2}\right) - 114 \, x \sin\left(1\right) + 56 \, x \sin\left(\frac{3}{2}\right) - 11 \, x \sin\left(2\right) - 48 \, \sin\left(\frac{1}{2}\right) + 36 \, \sin\left(1\right) - 16 \, \sin\left(\frac{3}{2}\right) + 3 \, \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 0.000373252230370591 None Polynom bei n= 8 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{630} \, {\left(8192 \, x^{7} \sin\left(\frac{1}{4}\right) - 28672 \, x^{7} \sin\left(\frac{1}{2}\right) + 57344 \, x^{7} \sin\left(\frac{3}{4}\right) - 71680 \, x^{7} \sin\left(1\right) + 57344 \, x^{7} \sin\left(\frac{5}{4}\right) - 28672 \, x^{7} \sin\left(\frac{3}{2}\right) + 8192 \, x^{7} \sin\left(\frac{7}{4}\right) - 1024 \, x^{7} \sin\left(2\right) - 71680 \, x^{6} \sin\left(\frac{1}{4}\right) + 243712 \, x^{6} \sin\left(\frac{1}{2}\right) - 473088 \, x^{6} \sin\left(\frac{3}{4}\right) + 573440 \, x^{6} \sin\left(1\right) - 444416 \, x^{6} \sin\left(\frac{5}{4}\right) + 215040 \, x^{6} \sin\left(\frac{3}{2}\right) - 59392 \, x^{6} \sin\left(\frac{7}{4}\right) + 7168 \, x^{6} \sin\left(2\right) + 261632 \, x^{5} \sin\left(\frac{1}{4}\right) - 856576 \, x^{5} \sin\left(\frac{1}{2}\right) + 1602048 \, x^{5} \sin\left(\frac{3}{4}\right) - 1872640 \, x^{5} \sin\left(1\right) + 1401344 \, x^{5} \sin\left(\frac{5}{4}\right) - 655872 \, x^{5} \sin\left(\frac{3}{2}\right) + 175616 \, x^{5} \sin\left(\frac{7}{4}\right) - 20608 \, x^{5} \sin\left(2\right) - 515200 \, x^{4} \sin\left(\frac{1}{4}\right) + 1603840 \, x^{4} \sin\left(\frac{1}{2}\right) - 2862720 \, x^{4} \sin\left(\frac{3}{4}\right) + 3207680 \, x^{4} \sin\left(1\right) - 2312576 \, x^{4} \sin\left(\frac{5}{4}\right) + 1048320 \, x^{4} \sin\left(\frac{3}{2}\right) - 273280 \, x^{4} \sin\left(\frac{7}{4}\right) + 31360 \, x^{4} \sin\left(2\right) + 589568 \, x^{3} \sin\left(\frac{1}{4}\right) - 1712368 \, x^{3} \sin\left(\frac{1}{2}\right) + 2881536 \, x^{3} \sin\left(\frac{3}{4}\right) - 3078040 \, x^{3} \sin\left(1\right) + 2137856 \, x^{3} \sin\left(\frac{5}{4}\right) - 941808 \, x^{3} \sin\left(\frac{3}{2}\right) + 240128 \, x^{3} \sin\left(\frac{7}{4}\right) - 27076 \, x^{3} \sin\left(2\right) - 390880 \, x^{2} \sin\left(\frac{1}{4}\right) + 1027768 \, x^{2} \sin\left(\frac{1}{2}\right) - 1606752 \, x^{2} \sin\left(\frac{3}{4}\right) + 1631840 \, x^{2} \sin\left(1\right) - 1095584 \, x^{2} \sin\left(\frac{5}{4}\right) + 471240 \, x^{2} \sin\left(\frac{3}{2}\right) - 118048 \, x^{2} \sin\left(\frac{7}{4}\right) + 13132 \, x^{2} \sin\left(2\right) + 138528 \, x \sin\left(\frac{1}{4}\right) - 312984 \, x \sin\left(\frac{1}{2}\right) + 448672 \, x \sin\left(\frac{3}{4}\right) - 435330 \, x \sin\left(1\right) + 284256 \, x \sin\left(\frac{5}{4}\right) - 120008 \, x \sin\left(\frac{3}{2}\right) + 29664 \, x \sin\left(\frac{7}{4}\right) - 3267 \, x \sin\left(2\right) - 20160 \, \sin\left(\frac{1}{4}\right) + 35280 \, \sin\left(\frac{1}{2}\right) - 47040 \, \sin\left(\frac{3}{4}\right) + 44100 \, \sin\left(1\right) - 28224 \, \sin\left(\frac{5}{4}\right) + 11760 \, \sin\left(\frac{3}{2}\right) - 2880 \, \sin\left(\frac{7}{4}\right) + 315 \, \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 0.0000245789030322370 None Polynom bei n= 16 ist: \newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{1277025750} \, {\left(274877906944 \, x^{15} \sin\left(\frac{1}{8}\right) - 2061584302080 \, x^{15} \sin\left(\frac{1}{4}\right) + 9620726743040 \, x^{15} \sin\left(\frac{3}{8}\right) - 31267361914880 \, x^{15} \sin\left(\frac{1}{2}\right) + 75041668595712 \, x^{15} \sin\left(\frac{5}{8}\right) - 137576392425472 \, x^{15} \sin\left(\frac{3}{4}\right) + 196537703464960 \, x^{15} \sin\left(\frac{7}{8}\right) - 221104916398080 \, x^{15} \sin\left(1\right) + 196537703464960 \, x^{15} \sin\left(\frac{9}{8}\right) - 137576392425472 \, x^{15} \sin\left(\frac{5}{4}\right) + 75041668595712 \, x^{15} \sin\left(\frac{11}{8}\right) - 31267361914880 \, x^{15} \sin\left(\frac{3}{2}\right) + 9620726743040 \, x^{15} \sin\left(\frac{13}{8}\right) - 2061584302080 \, x^{15} \sin\left(\frac{7}{4}\right) + 274877906944 \, x^{15} \sin\left(\frac{15}{8}\right) - 17179869184 \, x^{15} \sin\left(2\right) - 4638564679680 \, x^{14} \sin\left(\frac{1}{8}\right) + 34531537059840 \, x^{14} \sin\left(\frac{1}{4}\right) - 159944582103040 \, x^{14} \sin\left(\frac{3}{8}\right) + 515911471595520 \, x^{14} \sin\left(\frac{1}{2}\right) - 1228807323254784 \, x^{14} \sin\left(\frac{5}{8}\right) + 2235616376913920 \, x^{14} \sin\left(\frac{3}{4}\right) - 3169170468372480 \, x^{14} \sin\left(\frac{7}{8}\right) + 3537678662369280 \, x^{14} \sin\left(1\right) - 3120036042506240 \, x^{14} \sin\left(\frac{9}{8}\right) + 2166828180701184 \, x^{14} \sin\left(\frac{5}{4}\right) - 1172526071808000 \, x^{14} \sin\left(\frac{11}{8}\right) + 484644109680640 \, x^{14} \sin\left(\frac{3}{2}\right) - 147918673674240 \, x^{14} \sin\left(\frac{13}{8}\right) + 31439160606720 \, x^{14} \sin\left(\frac{7}{4}\right) - 4157528342528 \, x^{14} \sin\left(\frac{15}{8}\right) + 257698037760 \, x^{14} \sin\left(2\right) + 35927401431040 \, x^{13} \sin\left(\frac{1}{8}\right) - 265171280855040 \, x^{13} \sin\left(\frac{1}{4}\right) + 1217773552271360 \, x^{13} \sin\left(\frac{3}{8}\right) - 3894740768522240 \, x^{13} \sin\left(\frac{1}{2}\right) + 9198467033333760 \, x^{13} \sin\left(\frac{5}{8}\right) - 16595152336322560 \, x^{13} \sin\left(\frac{3}{4}\right) + 23329639581614080 \, x^{13} \sin\left(\frac{7}{8}\right) - 25827818046750720 \, x^{13} \sin\left(1\right) + 22592623193620480 \, x^{13} \sin\left(\frac{9}{8}\right) - 15563329393131520 \, x^{13} \sin\left(\frac{5}{4}\right) + 8354248261632000 \, x^{13} \sin\left(\frac{11}{8}\right) - 3425730339799040 \, x^{13} \sin\left(\frac{3}{2}\right) + 1037384925839360 \, x^{13} \sin\left(\frac{13}{8}\right) - 218785634058240 \, x^{13} \sin\left(\frac{7}{4}\right) + 28711856373760 \, x^{13} \sin\left(\frac{15}{8}\right) - 1766305300480 \, x^{13} \sin\left(2\right) - 169283451617280 \, x^{12} \sin\left(\frac{1}{8}\right) + 1237015005757440 \, x^{12} \sin\left(\frac{1}{4}\right) - 5625438105763840 \, x^{12} \sin\left(\frac{3}{8}\right) + 17819464976302080 \, x^{12} \sin\left(\frac{1}{2}\right) - 41691362969518080 \, x^{12} \sin\left(\frac{5}{8}\right) + 74527711334236160 \, x^{12} \sin\left(\frac{3}{4}\right) - 103835244775342080 \, x^{12} \sin\left(\frac{7}{8}\right) + 113951946288660480 \, x^{12} \sin\left(1\right) - 98831978316431360 \, x^{12} \sin\left(\frac{9}{8}\right) + 67519913845063680 \, x^{12} \sin\left(\frac{5}{4}\right) - 35953313505607680 \, x^{12} \sin\left(\frac{11}{8}\right) + 14628239850864640 \, x^{12} \sin\left(\frac{3}{2}\right) - 4396352683376640 \, x^{12} \sin\left(\frac{13}{8}\right) + 920432966369280 \, x^{12} \sin\left(\frac{7}{4}\right) - 119939646095360 \, x^{12} \sin\left(\frac{15}{8}\right) + 7328287948800 \, x^{12} \sin\left(2\right) + 542152849358848 \, x^{11} \sin\left(\frac{1}{8}\right) - 3915595854643200 \, x^{11} \sin\left(\frac{1}{4}\right) + 17606425538723840 \, x^{11} \sin\left(\frac{3}{8}\right) - 55167153204101120 \, x^{11} \sin\left(\frac{1}{2}\right) + 127727423805456384 \, x^{11} \sin\left(\frac{5}{8}\right) - 226042513545232384 \, x^{11} \sin\left(\frac{3}{4}\right) + 311913156601446400 \, x^{11} \sin\left(\frac{7}{8}\right) - 339163173963694080 \, x^{11} \sin\left(1\right) + 291583020173885440 \, x^{11} \sin\left(\frac{9}{8}\right) - 197538404739579904 \, x^{11} \sin\left(\frac{5}{4}\right) + 104348719591194624 \, x^{11} \sin\left(\frac{11}{8}\right) - 42134525915955200 \, x^{11} \sin\left(\frac{3}{2}\right) + 12571891717898240 \, x^{11} \sin\left(\frac{13}{8}\right) - 2614091914936320 \, x^{11} \sin\left(\frac{7}{4}\right) + 338426444382208 \, x^{11} \sin\left(\frac{15}{8}\right) - 20550504153088 \, x^{11} \sin\left(2\right) - 1248843320524800 \, x^{10} \sin\left(\frac{1}{8}\right) + 8895694236549120 \, x^{10} \sin\left(\frac{1}{4}\right) - 39479025357291520 \, x^{10} \sin\left(\frac{3}{8}\right) + 122181086934466560 \, x^{10} \sin\left(\frac{1}{2}\right) - 279605552609230848 \, x^{10} \sin\left(\frac{5}{8}\right) + 489432634401751040 \, x^{10} \sin\left(\frac{3}{4}\right) - 668453873060413440 \, x^{10} \sin\left(\frac{7}{8}\right) + 719886946758819840 \, x^{10} \sin\left(1\right) - 613346987391057920 \, x^{10} \sin\left(\frac{9}{8}\right) + 412041513636200448 \, x^{10} \sin\left(\frac{5}{4}\right) - 215955703049748480 \, x^{10} \sin\left(\frac{11}{8}\right) + 86562874662584320 \, x^{10} \sin\left(\frac{3}{2}\right) - 25652110892728320 \, x^{10} \sin\left(\frac{13}{8}\right) + 5299932349071360 \, x^{10} \sin\left(\frac{7}{4}\right) - 682062843478016 \, x^{10} \sin\left(\frac{15}{8}\right) + 41187268362240 \, x^{10} \sin\left(2\right) + 2135066091192320 \, x^{9} \sin\left(\frac{1}{8}\right) - 14959862737797120 \, x^{9} \sin\left(\frac{1}{4}\right) + 65386368210042880 \, x^{9} \sin\left(\frac{3}{8}\right) - 199530215369605120 \, x^{9} \sin\left(\frac{1}{2}\right) + 450736350827642880 \, x^{9} \sin\left(\frac{5}{8}\right) - 779656863080775680 \, x^{9} \sin\left(\frac{3}{4}\right) + 1053290488046551040 \, x^{9} \sin\left(\frac{7}{8}\right) - 1123074133587394560 \, x^{9} \sin\left(1\right) + 948172266159472640 \, x^{9} \sin\left(\frac{9}{8}\right) - 631679446836838400 \, x^{9} \sin\left(\frac{5}{4}\right) + 328550729515008000 \, x^{9} \sin\left(\frac{11}{8}\right) - 130776446842961920 \, x^{9} \sin\left(\frac{3}{2}\right) + 38506322518343680 \, x^{9} \sin\left(\frac{13}{8}\right) - 7908904686059520 \, x^{9} \sin\left(\frac{7}{4}\right) + 1012303674736640 \, x^{9} \sin\left(\frac{15}{8}\right) - 60823682416640 \, x^{9} \sin\left(2\right) - 2755264793149440 \, x^{8} \sin\left(\frac{1}{8}\right) + 18926144724664320 \, x^{8} \sin\left(\frac{1}{4}\right) - 81255293830430720 \, x^{8} \sin\left(\frac{3}{8}\right) + 244004233520087040 \, x^{8} \sin\left(\frac{1}{2}\right) - 543336199624458240 \, x^{8} \sin\left(\frac{5}{8}\right) + 927842453990932480 \, x^{8} \sin\left(\frac{3}{4}\right) - 1239206681961431040 \, x^{8} \sin\left(\frac{7}{8}\right) + 1307866207790039040 \, x^{8} \sin\left(1\right) - 1094142059572756480 \, x^{8} \sin\left(\frac{9}{8}\right) + 722985792755466240 \, x^{8} \sin\left(\frac{5}{4}\right) - 373289165808599040 \, x^{8} \sin\left(\frac{11}{8}\right) + 147604670940446720 \, x^{8} \sin\left(\frac{3}{2}\right) - 43202407816888320 \, x^{8} \sin\left(\frac{13}{8}\right) + 8825527208509440 \, x^{8} \sin\left(\frac{7}{4}\right) - 1124078664417280 \, x^{8} \sin\left(\frac{15}{8}\right) + 67236888576000 \, x^{8} \sin\left(2\right) + 2702248761884672 \, x^{7} \sin\left(\frac{1}{8}\right) - 18118390276546560 \, x^{7} \sin\left(\frac{1}{4}\right) + 76162254949580800 \, x^{7} \sin\left(\frac{3}{8}\right) - 224555101181931520 \, x^{7} \sin\left(\frac{1}{2}\right) + 492152198295453696 \, x^{7} \sin\left(\frac{5}{8}\right) - 828969918451490816 \, x^{7} \sin\left(\frac{3}{4}\right) + 1094053808919019520 \, x^{7} \sin\left(\frac{7}{8}\right) - 1142788404799641600 \, x^{7} \sin\left(1\right) + 947449838615920640 \, x^{7} \sin\left(\frac{9}{8}\right) - 621119518000357376 \, x^{7} \sin\left(\frac{5}{4}\right) + 318464720073916416 \, x^{7} \sin\left(\frac{11}{8}\right) - 125150211531304960 \, x^{7} \sin\left(\frac{3}{2}\right) + 36429077433548800 \, x^{7} \sin\left(\frac{13}{8}\right) - 7405253842821120 \, x^{7} \sin\left(\frac{7}{4}\right) + 939009365245952 \, x^{7} \sin\left(\frac{15}{8}\right) - 55942276662272 \, x^{7} \sin\left(2\right) - 2011072733429760 \, x^{6} \sin\left(\frac{1}{8}\right) + 13086806145853440 \, x^{6} \sin\left(\frac{1}{4}\right) - 53649038397194240 \, x^{6} \sin\left(\frac{3}{8}\right) + 154904572419717120 \, x^{6} \sin\left(\frac{1}{2}\right) - 333641971290980352 \, x^{6} \sin\left(\frac{5}{8}\right) + 553873902408386560 \, x^{6} \sin\left(\frac{3}{4}\right) - 722133404691578880 \, x^{6} \sin\left(\frac{7}{8}\right) + 746570893633044480 \, x^{6} \sin\left(1\right) - 613549419052810240 \, x^{6} \sin\left(\frac{9}{8}\right) + 399201943746557952 \, x^{6} \sin\left(\frac{5}{4}\right) - 203348105124003840 \, x^{6} \sin\left(\frac{11}{8}\right) + 79456805713725440 \, x^{6} \sin\left(\frac{3}{2}\right) - 23012633173770240 \, x^{6} \sin\left(\frac{13}{8}\right) + 4657209490053120 \, x^{6} \sin\left(\frac{7}{4}\right) - 588211268829184 \, x^{6} \sin\left(\frac{15}{8}\right) + 34918810967040 \, x^{6} \sin\left(2\right) + 1124493918679040 \, x^{5} \sin\left(\frac{1}{8}\right) - 7047383541219840 \, x^{5} \sin\left(\frac{1}{4}\right) + 28037340963573760 \, x^{5} \sin\left(\frac{3}{8}\right) - 79053837468336640 \, x^{5} \sin\left(\frac{1}{2}\right) + 167088464770805760 \, x^{5} \sin\left(\frac{5}{8}\right) - 273221517377768960 \, x^{5} \sin\left(\frac{3}{4}\right) + 351886048300666880 \, x^{5} \sin\left(\frac{7}{8}\right) - 360150980948478720 \, x^{5} \sin\left(1\right) + 293509680971386880 \, x^{5} \sin\left(\frac{9}{8}\right) - 189624514500861440 \, x^{5} \sin\left(\frac{5}{4}\right) + 96011052282163200 \, x^{5} \sin\left(\frac{11}{8}\right) - 37320915107607040 \, x^{5} \sin\left(\frac{3}{2}\right) + 10760201455144960 \, x^{5} \sin\left(\frac{13}{8}\right) - 2168968470090240 \, x^{5} \sin\left(\frac{7}{4}\right) + 272981881303040 \, x^{5} \sin\left(\frac{15}{8}\right) - 16154753713280 \, x^{5} \sin\left(2\right) - 463008406049280 \, x^{4} \sin\left(\frac{1}{8}\right) + 2764930208826240 \, x^{4} \sin\left(\frac{1}{4}\right) - 10610952244605440 \, x^{4} \sin\left(\frac{3}{8}\right) + 29129185360154880 \, x^{4} \sin\left(\frac{1}{2}\right) - 60344359344622080 \, x^{4} \sin\left(\frac{5}{8}\right) + 97170719981695360 \, x^{4} \sin\left(\frac{3}{4}\right) - 123652362044090880 \, x^{4} \sin\left(\frac{7}{8}\right) + 125345755147092480 \, x^{4} \sin\left(1\right) - 101354263214364160 \, x^{4} \sin\left(\frac{9}{8}\right) + 65056214888945280 \, x^{4} \sin\left(\frac{5}{4}\right) - 32759452938401280 \, x^{4} \sin\left(\frac{11}{8}\right) + 12674731432912640 \, x^{4} \sin\left(\frac{3}{2}\right) - 3639627741335040 \, x^{4} \sin\left(\frac{13}{8}\right) + 731081271473280 \, x^{4} \sin\left(\frac{7}{4}\right) - 91729118440960 \, x^{4} \sin\left(\frac{15}{8}\right) + 5413626691200 \, x^{4} \sin\left(2\right) + 135587986177536 \, x^{3} \sin\left(\frac{1}{8}\right) - 759747724796160 \, x^{3} \sin\left(\frac{1}{4}\right) + 2792134200952320 \, x^{3} \sin\left(\frac{3}{8}\right) - 7441941521130480 \, x^{3} \sin\left(\frac{1}{2}\right) + 15100457492510208 \, x^{3} \sin\left(\frac{5}{8}\right) - 23950710499043328 \, x^{3} \sin\left(\frac{3}{4}\right) + 30130969619013120 \, x^{3} \sin\left(\frac{7}{8}\right) - 30271879561449240 \, x^{3} \sin\left(1\right) + 24303240291432960 \, x^{3} \sin\left(\frac{9}{8}\right) - 15508481874133248 \, x^{3} \sin\left(\frac{5}{4}\right) + 7771434292597248 \, x^{3} \sin\left(\frac{11}{8}\right) - 2994437051838960 \, x^{3} \sin\left(\frac{3}{2}\right) + 856846213009920 \, x^{3} \sin\left(\frac{13}{8}\right) - 171588051924480 \, x^{3} \sin\left(\frac{7}{4}\right) + 21471939856896 \, x^{3} \sin\left(\frac{15}{8}\right) - 1264248925956 \, x^{3} \sin\left(2\right) - 26590376165760 \, x^{2} \sin\left(\frac{1}{8}\right) + 136604627085600 \, x^{2} \sin\left(\frac{1}{4}\right) - 476810279971200 \, x^{2} \sin\left(\frac{3}{8}\right) + 1231576206751800 \, x^{2} \sin\left(\frac{1}{2}\right) - 2448326788742016 \, x^{2} \sin\left(\frac{5}{8}\right) + 3828173781912480 \, x^{2} \sin\left(\frac{3}{4}\right) - 4765696806499200 \, x^{2} \sin\left(\frac{7}{8}\right) + 4749702564578400 \, x^{2} \sin\left(1\right) - 3789149895273600 \, x^{2} \sin\left(\frac{9}{8}\right) + 2405604313528416 \, x^{2} \sin\left(\frac{5}{4}\right) - 1200390569239680 \, x^{2} \sin\left(\frac{11}{8}\right) + 460891389558600 \, x^{2} \sin\left(\frac{3}{2}\right) - 131485509187200 \, x^{2} \sin\left(\frac{13}{8}\right) + 26262467416800 \, x^{2} \sin\left(\frac{7}{4}\right) - 3278987206272 \, x^{2} \sin\left(\frac{15}{8}\right) + 192681800460 \, x^{2} \sin\left(2\right) + 3113218281600 \, x \sin\left(\frac{1}{8}\right) - 14126457996000 \, x \sin\left(\frac{1}{4}\right) + 46491680592000 \, x \sin\left(\frac{3}{8}\right) - 116422387263000 \, x \sin\left(\frac{1}{2}\right) + 227100934569600 \, x \sin\left(\frac{5}{8}\right) - 350595822376800 \, x \sin\left(\frac{3}{4}\right) + 432481235472000 \, x \sin\left(\frac{7}{8}\right) - 428071619225250 \, x \sin\left(1\right) + 339672308976000 \, x \sin\left(\frac{9}{8}\right) - 214720766900640 \, x \sin\left(\frac{5}{4}\right) + 106768144828800 \, x \sin\left(\frac{11}{8}\right) - 40873406301000 \, x \sin\left(\frac{3}{2}\right) + 11631583152000 \, x \sin\left(\frac{13}{8}\right) - 2318296788000 \, x \sin\left(\frac{7}{4}\right) + 288914290560 \, x \sin\left(\frac{15}{8}\right) - 16949855475 \, x \sin\left(2\right) - 163459296000 \, \sin\left(\frac{1}{8}\right) + 612972360000 \, \sin\left(\frac{1}{4}\right) - 1907025120000 \, \sin\left(\frac{3}{8}\right) + 4648373730000 \, \sin\left(\frac{1}{2}\right) - 8924877561600 \, \sin\left(\frac{5}{8}\right) + 13635229608000 \, \sin\left(\frac{3}{4}\right) - 16696199520000 \, \sin\left(\frac{7}{8}\right) + 16435321402500 \, \sin\left(1\right) - 12985932960000 \, \sin\left(\frac{9}{8}\right) + 8181137764800 \, \sin\left(\frac{5}{4}\right) - 4056762528000 \, \sin\left(\frac{11}{8}\right) + 1549457910000 \, \sin\left(\frac{3}{2}\right) - 440082720000 \, \sin\left(\frac{13}{8}\right) + 87567480000 \, \sin\left(\frac{7}{4}\right) - 10897286400 \, \sin\left(\frac{15}{8}\right) + 638512875 \, \sin\left(2\right)\right)} x None Der Fehler ist: Der Fehler ist: 2.19263792655727e-15 + 35.8084947935008*I None |
#mit gleichverteilten Stützstellen oszilliert die Funktion bei hoher Stützstellen Anzahl
Funktion2=plot(sin(x),0,2)
Pn2mit2Stst=plot(pn2(g,2),0,2,color='yellow')
Pn2mit8Stst=plot(pn2(g,8),0,2,color='red')
Pn2mit16Stst=plot(pn2(g,16),0,2,color='black')
Pn2mit32Stst=plot(pn2(g,32),0,2,color='green')
Pn2mit64Stst=plot(pn2(g,64),0,2,color='purple')
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show(Funktion2+Pn2mit2Stst+Pn2mit8Stst+Pn2mit16Stst+Pn2mit32Stst)
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show(Pn2mit64Stst)
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Pn2mit70Stst=plot(pn2(g,70),0,2,color='purple')
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show(Pn2mit70Stst)
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#############################################################################################################################################
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#definiere Fehler für Tschebyschef Stützstellen neu
def fehlertscheb2(n):
poly= pntscheb2(g,n)
print 'Der Fehler ist:', sqrt(integral((sin(x) - poly)^2,x,0,2).n())
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#Ausgabe für Tschebyscheff Stützstellen neu
for i in range(1,5):
print 'Polynom bei n=',2^i,'ist:', pntscheb2(g,2^i)
print 'Der Fehler ist:', fehlertscheb2(2^i)
Polynom bei n= 2 ist: 0.133574166452703*(-1.15470053837925*x + 1.15470053837925)*(-0.577350269189626*x + 1.07735026918963) + 0.841470984807897*(-1.15470053837925*x + 2.15470053837925)*(1.15470053837925*x - 0.154700538379252) + 0.956735515407288*(0.577350269189626*x - 0.0773502691896258)*(1.15470053837925*x - 1.15470053837925) Der Fehler ist: Der Fehler ist: 0.0215375647235925 None Polynom bei n= 4 ist: 0.0489239456480500*(-2.75276384094235*x + 1.13472985219245)*(-1.05146222423827*x + 1.05146222423827)*(-0.649839392465813*x + 1.03180540371592)*(-0.525731112119134*x + 1.02573111211913) + 0.999855691676168*(-2.75276384094235*x + 5.37079782969224)*(0.649839392465813*x - 0.0318054037159178)*(0.850650808352040*x - 0.350650808352040)*(1.70130161670408*x - 1.70130161670408) + 0.400639539953362*(-1.70130161670408*x + 1.70130161670408)*(-0.850650808352040*x + 1.35065080835204)*(-0.649839392465813*x + 1.26787338121571)*(2.75276384094235*x - 0.134729852192452) + 0.841470984807897*(-1.70130161670408*x + 2.70130161670408)*(-1.05146222423827*x + 2.05146222423827)*(1.05146222423827*x - 0.0514622242382673)*(1.70130161670408*x - 0.701301616704080) + 0.928568094531391*(0.525731112119134*x - 0.0257311121191336)*(0.649839392465813*x - 0.267873381215708)*(1.05146222423827*x - 1.05146222423827)*(2.75276384094235*x - 4.37079782969224) Der Fehler ist: Der Fehler ist: 0.000273107806734461 None Polynom bei n= 8 ist: 0.0151916625883740*(-8.41875923907233*x + 1.12789986969074)*(-2.92380440016309*x + 1.04441915859127)*(-1.55572382686041*x + 1.02363494062246)*(-1.01542661188575*x + 1.01542661188575)*(-0.753677249898091*x + 1.01145005092953)*(-0.614403323404584*x + 1.00933416703928)*(-0.540297214974667*x + 1.00820832873671)*(-0.507713305942872*x + 1.00771330594287) + 0.956735515407288*(-8.41875923907232*x + 16.7096186084539)*(0.540297214974667*x - 0.00820832873671129)*(0.577350269189626*x - 0.0773502691896258)*(0.662772650468815*x - 0.236750602708353)*(0.827783358328008*x - 0.544664775470059)*(1.15470053837925*x - 1.15470053837925)*(1.90837778827734*x - 2.56108143294348)*(4.47952822702350*x - 7.35891346859531) + 0.133574166452703*(-4.47952822702350*x + 1.60014298545168)*(-1.90837778827734*x + 1.25567414361120)*(-1.15470053837925*x + 1.15470053837925)*(-0.827783358328008*x + 1.11090194118596)*(-0.662772650468815*x + 1.08879469822928)*(-0.577350269189626*x + 1.07735026918963)*(-0.540297214974667*x + 1.07238610121262)*(8.41875923907233*x - 0.127899869690743) + 0.997409746602299*(-4.47952822702350*x + 8.35891346859531)*(-2.92380440016309*x + 5.80318964173490)*(0.614403323404584*x - 0.00933416703928268)*(0.662772650468815*x - 0.0887946982292769)*(0.777861913430206*x - 0.277861913430206)*(1.01542661188575*x - 0.668130256551884)*(1.55572382686041*x - 1.55572382686041)*(3.32482768864425*x - 4.46198573124751) + 0.973944668454592*(-3.32482768864425*x + 5.46198573124751)*(-1.90837778827734*x + 3.56108143294348)*(-1.55572382686041*x + 3.08781271309837)*(0.753677249898091*x - 0.0114500509295316)*(0.827783358328008*x - 0.110901941185956)*(1.01542661188574*x - 0.362722967219606)*(1.46190220008154*x - 0.961902200081544)*(2.92380440016309*x - 2.92380440016309) + 0.349663952882940*(-3.32482768864425*x + 2.18766964604099)*(-1.55572382686041*x + 1.55572382686041)*(-1.01542661188574*x + 1.36272296721961)*(-0.777861913430206*x + 1.27786191343021)*(-0.662772650468815*x + 1.23675060270835)*(-0.614403323404584*x + 1.21947247976989)*(2.92380440016309*x - 0.0444191585912706)*(4.47952822702350*x - 0.600142985451683) + 0.611519704467024*(-2.92380440016309*x + 2.92380440016309)*(-1.46190220008154*x + 1.96190220008154)*(-1.01542661188575*x + 1.66813025655188)*(-0.827783358328008*x + 1.54466477547006)*(-0.753677249898091*x + 1.49590444886665)*(1.55572382686041*x - 0.0236349406224563)*(1.90837778827734*x - 0.255674143611203)*(3.32482768864425*x - 1.18766964604099) + 0.841470984807897*(-2.92380440016309*x + 3.92380440016309)*(-1.55572382686041*x + 2.55572382686041)*(-1.15470053837925*x + 2.15470053837925)*(-1.01542661188574*x + 2.01542661188574)*(1.01542661188575*x - 0.0154266118857450)*(1.15470053837925*x - 0.154700538379252)*(1.55572382686041*x - 0.555723826860412)*(2.92380440016309*x - 1.92380440016309) + 0.915514456262790*(0.507713305942872*x - 0.00771330594287251)*(0.540297214974667*x - 0.0723861012126234)*(0.614403323404584*x - 0.219472479769886)*(0.753677249898091*x - 0.495904448866650)*(1.01542661188574*x - 1.01542661188574)*(1.55572382686041*x - 2.08781271309837)*(2.92380440016309*x - 4.80318964173490)*(8.41875923907232*x - 15.7096186084539) Der Fehler ist: Der Fehler ist: 0.0000165508908583167*I None Polynom bei n= 16 ist: 0.924517235797106*(-29.4911017352398*x + 58.8563996296119)*(0.510840072448893*x - 0.00217915369049880)*(0.519844738543908*x - 0.0198447385439077)*(0.538506170611210*x - 0.0564552145118686)*(0.568232548933506*x - 0.114773185783207)*(0.611425854288155*x - 0.199510919841350)*(0.671926594931823*x - 0.318202824267046)*(0.755819445409581*x - 0.482785969613174)*(0.872923954755040*x - 0.712524598978268)*(1.03968947708782*x - 1.03968947708782)*(1.28522128800976*x - 1.52138007996914)*(1.66504608567649*x - 2.26653010794466)*(2.29677302315457*x - 3.50586821337219)*(3.47065561255052*x - 5.80882117932328)*(6.10469245155126*x - 10.9763421951368)*(15.0009709038443*x - 28.4292893916511) + 0.00426581076726590*(-29.4911017352397*x + 1.12580384086774)*(-9.94323556560997*x + 1.04241608997984)*(-5.05773533823431*x + 1.02157540729928)*(-3.10521847114350*x + 1.01324631456330)*(-2.13082401398095*x + 1.00908971958995)*(-1.57606273371134*x + 1.00672320576998)*(-1.23155036189212*x + 1.00525357672762)*(-1.00428409891567*x + 1.00428409891567)*(-0.847828592283513*x + 1.00361668730671)*(-0.736932794743637*x + 1.00314362538478)*(-0.656958424493676*x + 1.00280246882038)*(-0.599006911254878*x + 1.00255525788147)*(-0.557490852972612*x + 1.00237815769591)*(-0.528849404638922*x + 1.00225597832667)*(-0.510840072448893*x + 1.00217915369050)*(-0.502142049457837*x + 1.00214204945784) + 0.947852670301149*(-15.0009709038443*x + 29.4292893916511)*(-9.94323556560999*x + 19.8440550412401)*(0.528849404638922*x - 0.00225597832666562)*(0.538506170611210*x - 0.0205571267105511)*(0.558557309966453*x - 0.0585573099664532)*(0.590604480144856*x - 0.119291930480371)*(0.637405937327926*x - 0.207988334115652)*(0.703435001162088*x - 0.333124192056695)*(0.795921724120067*x - 0.508401634344383)*(0.926858956070583*x - 0.756549069808644)*(1.11711461993291*x - 1.11711461993291)*(1.40565172786311*x - 1.66393955507599)*(1.87293406534249*x - 2.54951588776549)*(2.71200319899344*x - 4.13968890876986)*(4.51533219568122*x - 7.55729182552871)*(10.2937778233588*x - 18.5083898601943) + 0.0381650857052867*(-15.0009709038443*x + 1.57265241603751)*(-6.10469245155126*x + 1.23304270796572)*(-3.47065561255052*x + 1.13249004577776)*(-2.29677302315457*x + 1.08767783293695)*(-1.66504608567649*x + 1.06356206340831)*(-1.28522128800976*x + 1.04906249605037)*(-1.03968947708782*x + 1.03968947708782)*(-0.872923954755040*x + 1.03332331053181)*(-0.755819445409580*x + 1.02885292120599)*(-0.671926594931823*x + 1.02565036559660)*(-0.611425854288155*x + 1.02334078873496)*(-0.568232548933506*x + 1.02169191208381)*(-0.538506170611210*x + 1.02055712671055)*(-0.519844738543908*x + 1.01984473854391)*(-0.510840072448893*x + 1.01950099120729)*(29.4911017352397*x - 0.125803840867736) + 0.104644775394141*(-10.2937778233588*x + 2.07916578652318)*(-4.51533219568122*x + 1.47337256583374)*(-2.71200319899344*x + 1.28431748921701)*(-1.87293406534249*x + 1.19635224291949)*(-1.40565172786312*x + 1.14736390065024)*(-1.11711461993291*x + 1.11711461993291)*(-0.926858956070583*x + 1.09716884233252)*(-0.795921724120067*x + 1.08344181389575)*(-0.703435001162088*x + 1.07374581026748)*(-0.637405937327927*x + 1.06682354054020)*(-0.590604480144856*x + 1.06191702980934)*(-0.558557309966453*x + 1.05855730996645)*(-0.538506170611210*x + 1.05645521451187)*(-0.528849404638923*x + 1.05544283095118)*(9.94323556560997*x - 0.0424160899798354)*(15.0009709038443*x - 0.572652416037510) + 0.974296206412599*(-10.2937778233588*x + 19.5083898601943)*(-6.10469245155126*x + 11.9763421951368)*(-5.05773533823432*x + 10.0938952691693)*(0.557490852972612*x - 0.00237815769591202)*(0.568232548933506*x - 0.0216919120838062)*(0.590604480144856*x - 0.0619170298093412)*(0.626552889972155*x - 0.126552889972155)*(0.679480365874805*x - 0.221717403441580)*(0.755030737626759*x - 0.357558273379019)*(0.862620080497254*x - 0.551005765331930)*(1.01857188073873*x - 0.831409788791472)*(1.25310577994431*x - 1.25310577994431)*(1.62795469238180*x - 1.92709058213418)*(2.28950538692543*x - 3.11657012764284)*(3.68208760742655*x - 5.62045695050802)*(8.04365558072790*x - 13.4626313044576) + 0.200612188272927*(-8.04365558072791*x + 2.62467985699820)*(-3.68208760742655*x + 1.74371826434508)*(-2.28950538692543*x + 1.46244064620803)*(-1.62795469238180*x + 1.32881880262942)*(-1.25310577994431*x + 1.25310577994431)*(-1.01857188073873*x + 1.20573397268599)*(-0.862620080497254*x + 1.17423439566258)*(-0.755030737626759*x + 1.15250320187450)*(-0.679480365874805*x + 1.13724332830803)*(-0.626552889972155*x + 1.12655288997215)*(-0.590604480144856*x + 1.11929193048037)*(-0.568232548933506*x + 1.11477318578321)*(-0.557490852972612*x + 1.11260354824931)*(5.05773533823431*x - 0.0215754072992818)*(6.10469245155126*x - 0.233042707965716)*(10.2937778233588*x - 1.07916578652318) + 0.994710534957717*(-8.04365558072790*x + 14.4626313044576)*(-4.51533219568122*x + 8.55729182552871)*(-3.47065561255052*x + 6.80882117932328)*(-3.10521847114350*x + 6.19719062772370)*(0.599006911254878*x - 0.00255525788146924)*(0.611425854288155*x - 0.0233407887349600)*(0.637405937327927*x - 0.0668235405402013)*(0.679480365874805*x - 0.137243328308031)*(0.742174904521598*x - 0.242174904521598)*(0.833244588254671*x - 0.394597837453913)*(0.966242100365167*x - 0.617195194089080)*(1.16625534196685*x - 0.951956485229441)*(1.48434980904320*x - 1.48434980904320)*(2.04104073341934*x - 2.41608098402912)*(3.20047134023098*x - 4.35661493976025)*(6.79054980078360*x - 10.3653136195365) + 0.320544588125103*(-6.79054980078361*x + 3.21578598203069)*(-3.20047134023098*x + 2.04432774070171)*(-2.04104073341934*x + 1.66600048280956)*(-1.48434980904320*x + 1.48434980904320)*(-1.16625534196685*x + 1.38055419870426)*(-0.966242100365167*x + 1.31528900664125)*(-0.833244588254671*x + 1.27189133905543)*(-0.742174904521598*x + 1.24217490452160)*(-0.679480365874805*x + 1.22171740344158)*(-0.637405937327926*x + 1.20798833411565)*(-0.611425854288155*x + 1.19951091984135)*(-0.599006911254878*x + 1.19545856462829)*(3.10521847114350*x - 0.0132463145633008)*(3.47065561255052*x - 0.132490045777762)*(4.51533219568122*x - 0.473372565833740)*(8.04365558072791*x - 1.62467985699820) + 0.999016071874724*(-6.79054980078360*x + 11.3653136195365)*(-3.68208760742655*x + 6.62045695050802)*(-2.71200319899344*x + 5.13968890876986)*(-2.29677302315457*x + 4.50586821337219)*(-2.13082401398095*x + 4.25255830837195)*(0.656958424493676*x - 0.00280246882038193)*(0.671926594931823*x - 0.0256503655966001)*(0.703435001162088*x - 0.0737458102674813)*(0.755030737626759*x - 0.152503201874499)*(0.833244588254671*x - 0.271891339055430)*(0.949789992441032*x - 0.449789992441032)*(1.12653991506528*x - 0.719586759120762)*(1.40809039036728*x - 1.14935446009514)*(1.89957998488206*x - 1.89957998488206)*(2.91815186562080*x - 3.45436086384414)*(6.05361700603997*x - 8.24043569976073) + 0.978123653141135*(-6.05361700603997*x + 9.24043569976073)*(-3.20047134023098*x + 5.35661493976025)*(-2.28950538692543*x + 4.11657012764284)*(-1.87293406534249*x + 3.54951588776549)*(-1.66504608567649*x + 3.26653010794466)*(-1.57606273371134*x + 3.14540226165271)*(0.736932794743637*x - 0.00314362538478391)*(0.755819445409580*x - 0.0288529212059873)*(0.795921724120067*x - 0.0834418138957520)*(0.862620080497254*x - 0.174234395662578)*(0.966242100365167*x - 0.315289006641254)*(1.12653991506528*x - 0.533493071009790)*(1.38411497565444*x - 0.884114975654438)*(1.83489206679198*x - 1.49773153427350)*(2.76822995130888*x - 2.76822995130888)*(5.63405203655611*x - 6.66930638162676) + 0.456064366570132*(-6.05361700603996*x + 3.86679831231920)*(-2.91815186562080*x + 2.38194286739745)*(-1.89957998488206*x + 1.89957998488206)*(-1.40809039036728*x + 1.66682632063941)*(-1.12653991506528*x + 1.53349307100979)*(-0.949789992441032*x + 1.44978999244103)*(-0.833244588254671*x + 1.39459783745391)*(-0.755030737626759*x + 1.35755827337902)*(-0.703435001162088*x + 1.33312419205669)*(-0.671926594931823*x + 1.31820282426705)*(-0.656958424493676*x + 1.31111438016697)*(2.13082401398095*x - 0.00908971958994975)*(2.29677302315457*x - 0.0876778329369457)*(2.71200319899344*x - 0.284317489217014)*(3.68208760742655*x - 0.743718264345084)*(6.79054980078361*x - 2.21578598203069) + 0.596199046078406*(-5.63405203655611*x + 4.59879769148546)*(-2.76822995130888*x + 2.76822995130888)*(-1.83489206679198*x + 2.17205259931046)*(-1.38411497565444*x + 1.88411497565444)*(-1.12653991506528*x + 1.71958675912076)*(-0.966242100365167*x + 1.61719519408908)*(-0.862620080497254*x + 1.55100576533193)*(-0.795921724120067*x + 1.50840163434438)*(-0.755819445409581*x + 1.48278596961317)*(-0.736932794743637*x + 1.47072196410249)*(1.57606273371134*x - 0.00672320576997863)*(1.66504608567649*x - 0.0635620634083151)*(1.87293406534249*x - 0.196352242919489)*(2.28950538692543*x - 0.462440646208027)*(3.20047134023098*x - 1.04432774070171)*(6.05361700603996*x - 2.86679831231920) + 0.926027794020423*(-5.63405203655611*x + 7.66930638162676)*(-2.91815186562080*x + 4.45436086384414)*(-2.04104073341934*x + 3.41608098402912)*(-1.62795469238180*x + 2.92709058213418)*(-1.40565172786311*x + 2.66393955507599)*(-1.28522128800976*x + 2.52138007996914)*(-1.23155036189212*x + 2.45784714705662)*(0.847828592283513*x - 0.00361668730671057)*(0.872923954755040*x - 0.0333233105318129)*(0.926858956070583*x - 0.0971688423325229)*(1.01857188073873*x - 0.205733972685990)*(1.16625534196685*x - 0.380554198704257)*(1.40809039036728*x - 0.666826320639411)*(1.83489206679198*x - 1.17205259931046)*(2.72109557587590*x - 2.22109557587590)*(5.44219115175180*x - 5.44219115175180) + 0.728582695607967*(-5.44219115175180*x + 5.44219115175180)*(-2.72109557587590*x + 3.22109557587590)*(-1.83489206679198*x + 2.49773153427350)*(-1.40809039036728*x + 2.14935446009514)*(-1.16625534196685*x + 1.95195648522944)*(-1.01857188073873*x + 1.83140978879147)*(-0.926858956070583*x + 1.75654906980864)*(-0.872923954755040*x + 1.71252459897827)*(-0.847828592283513*x + 1.69204049726032)*(1.23155036189212*x - 0.00525357672761828)*(1.28522128800976*x - 0.0490624960503736)*(1.40565172786312*x - 0.147363900650239)*(1.62795469238180*x - 0.328818802629421)*(2.04104073341934*x - 0.666000482809556)*(2.91815186562080*x - 1.38194286739745)*(5.63405203655611*x - 3.59879769148546) + 0.841470984807897*(-5.44219115175180*x + 6.44219115175180)*(-2.76822995130888*x + 3.76822995130888)*(-1.89957998488206*x + 2.89957998488206)*(-1.48434980904320*x + 2.48434980904320)*(-1.25310577994431*x + 2.25310577994431)*(-1.11711461993291*x + 2.11711461993291)*(-1.03968947708782*x + 2.03968947708782)*(-1.00428409891567*x + 2.00428409891567)*(1.00428409891567*x - 0.00428409891567443)*(1.03968947708782*x - 0.0396894770878154)*(1.11711461993291*x - 0.117114619932907)*(1.25310577994431*x - 0.253105779944310)*(1.48434980904320*x - 0.484349809043196)*(1.89957998488206*x - 0.899579984882064)*(2.76822995130888*x - 1.76822995130888)*(5.44219115175180*x - 4.44219115175180) + 0.911064357137178*(0.502142049457837*x - 0.00214204945783722)*(0.510840072448893*x - 0.0195009912072870)*(0.528849404638923*x - 0.0554428309511795)*(0.557490852972612*x - 0.112603548249313)*(0.599006911254878*x - 0.195458564628287)*(0.656958424493676*x - 0.311114380166970)*(0.736932794743637*x - 0.470721964102491)*(0.847828592283513*x - 0.692040497260316)*(1.00428409891567*x - 1.00428409891567)*(1.23155036189212*x - 1.45784714705662)*(1.57606273371134*x - 2.14540226165271)*(2.13082401398095*x - 3.25255830837195)*(3.10521847114350*x - 5.19719062772370)*(5.05773533823432*x - 9.09389526916935)*(9.94323556560999*x - 18.8440550412401)*(29.4911017352398*x - 57.8563996296119) Der Fehler ist: Der Fehler ist: 1.58113883008419 None Polynom bei n= 2 ist: 0.133574166452703*(-1.15470053837925*x + 1.15470053837925)*(-0.577350269189626*x + 1.07735026918963) + 0.841470984807897*(-1.15470053837925*x + 2.15470053837925)*(1.15470053837925*x - 0.154700538379252) + 0.956735515407288*(0.577350269189626*x - 0.0773502691896258)*(1.15470053837925*x - 1.15470053837925) Der Fehler ist: Der Fehler ist: 0.0215375647235925 None Polynom bei n= 4 ist: 0.0489239456480500*(-2.75276384094235*x + 1.13472985219245)*(-1.05146222423827*x + 1.05146222423827)*(-0.649839392465813*x + 1.03180540371592)*(-0.525731112119134*x + 1.02573111211913) + 0.999855691676168*(-2.75276384094235*x + 5.37079782969224)*(0.649839392465813*x - 0.0318054037159178)*(0.850650808352040*x - 0.350650808352040)*(1.70130161670408*x - 1.70130161670408) + 0.400639539953362*(-1.70130161670408*x + 1.70130161670408)*(-0.850650808352040*x + 1.35065080835204)*(-0.649839392465813*x + 1.26787338121571)*(2.75276384094235*x - 0.134729852192452) + 0.841470984807897*(-1.70130161670408*x + 2.70130161670408)*(-1.05146222423827*x + 2.05146222423827)*(1.05146222423827*x - 0.0514622242382673)*(1.70130161670408*x - 0.701301616704080) + 0.928568094531391*(0.525731112119134*x - 0.0257311121191336)*(0.649839392465813*x - 0.267873381215708)*(1.05146222423827*x - 1.05146222423827)*(2.75276384094235*x - 4.37079782969224) Der Fehler ist: Der Fehler ist: 0.000273107806734461 None Polynom bei n= 8 ist: 0.0151916625883740*(-8.41875923907233*x + 1.12789986969074)*(-2.92380440016309*x + 1.04441915859127)*(-1.55572382686041*x + 1.02363494062246)*(-1.01542661188575*x + 1.01542661188575)*(-0.753677249898091*x + 1.01145005092953)*(-0.614403323404584*x + 1.00933416703928)*(-0.540297214974667*x + 1.00820832873671)*(-0.507713305942872*x + 1.00771330594287) + 0.956735515407288*(-8.41875923907232*x + 16.7096186084539)*(0.540297214974667*x - 0.00820832873671129)*(0.577350269189626*x - 0.0773502691896258)*(0.662772650468815*x - 0.236750602708353)*(0.827783358328008*x - 0.544664775470059)*(1.15470053837925*x - 1.15470053837925)*(1.90837778827734*x - 2.56108143294348)*(4.47952822702350*x - 7.35891346859531) + 0.133574166452703*(-4.47952822702350*x + 1.60014298545168)*(-1.90837778827734*x + 1.25567414361120)*(-1.15470053837925*x + 1.15470053837925)*(-0.827783358328008*x + 1.11090194118596)*(-0.662772650468815*x + 1.08879469822928)*(-0.577350269189626*x + 1.07735026918963)*(-0.540297214974667*x + 1.07238610121262)*(8.41875923907233*x - 0.127899869690743) + 0.997409746602299*(-4.47952822702350*x + 8.35891346859531)*(-2.92380440016309*x + 5.80318964173490)*(0.614403323404584*x - 0.00933416703928268)*(0.662772650468815*x - 0.0887946982292769)*(0.777861913430206*x - 0.277861913430206)*(1.01542661188575*x - 0.668130256551884)*(1.55572382686041*x - 1.55572382686041)*(3.32482768864425*x - 4.46198573124751) + 0.973944668454592*(-3.32482768864425*x + 5.46198573124751)*(-1.90837778827734*x + 3.56108143294348)*(-1.55572382686041*x + 3.08781271309837)*(0.753677249898091*x - 0.0114500509295316)*(0.827783358328008*x - 0.110901941185956)*(1.01542661188574*x - 0.362722967219606)*(1.46190220008154*x - 0.961902200081544)*(2.92380440016309*x - 2.92380440016309) + 0.349663952882940*(-3.32482768864425*x + 2.18766964604099)*(-1.55572382686041*x + 1.55572382686041)*(-1.01542661188574*x + 1.36272296721961)*(-0.777861913430206*x + 1.27786191343021)*(-0.662772650468815*x + 1.23675060270835)*(-0.614403323404584*x + 1.21947247976989)*(2.92380440016309*x - 0.0444191585912706)*(4.47952822702350*x - 0.600142985451683) + 0.611519704467024*(-2.92380440016309*x + 2.92380440016309)*(-1.46190220008154*x + 1.96190220008154)*(-1.01542661188575*x + 1.66813025655188)*(-0.827783358328008*x + 1.54466477547006)*(-0.753677249898091*x + 1.49590444886665)*(1.55572382686041*x - 0.0236349406224563)*(1.90837778827734*x - 0.255674143611203)*(3.32482768864425*x - 1.18766964604099) + 0.841470984807897*(-2.92380440016309*x + 3.92380440016309)*(-1.55572382686041*x + 2.55572382686041)*(-1.15470053837925*x + 2.15470053837925)*(-1.01542661188574*x + 2.01542661188574)*(1.01542661188575*x - 0.0154266118857450)*(1.15470053837925*x - 0.154700538379252)*(1.55572382686041*x - 0.555723826860412)*(2.92380440016309*x - 1.92380440016309) + 0.915514456262790*(0.507713305942872*x - 0.00771330594287251)*(0.540297214974667*x - 0.0723861012126234)*(0.614403323404584*x - 0.219472479769886)*(0.753677249898091*x - 0.495904448866650)*(1.01542661188574*x - 1.01542661188574)*(1.55572382686041*x - 2.08781271309837)*(2.92380440016309*x - 4.80318964173490)*(8.41875923907232*x - 15.7096186084539) Der Fehler ist: Der Fehler ist: 0.0000165508908583167*I None Polynom bei n= 16 ist: 0.924517235797106*(-29.4911017352398*x + 58.8563996296119)*(0.510840072448893*x - 0.00217915369049880)*(0.519844738543908*x - 0.0198447385439077)*(0.538506170611210*x - 0.0564552145118686)*(0.568232548933506*x - 0.114773185783207)*(0.611425854288155*x - 0.199510919841350)*(0.671926594931823*x - 0.318202824267046)*(0.755819445409581*x - 0.482785969613174)*(0.872923954755040*x - 0.712524598978268)*(1.03968947708782*x - 1.03968947708782)*(1.28522128800976*x - 1.52138007996914)*(1.66504608567649*x - 2.26653010794466)*(2.29677302315457*x - 3.50586821337219)*(3.47065561255052*x - 5.80882117932328)*(6.10469245155126*x - 10.9763421951368)*(15.0009709038443*x - 28.4292893916511) + 0.00426581076726590*(-29.4911017352397*x + 1.12580384086774)*(-9.94323556560997*x + 1.04241608997984)*(-5.05773533823431*x + 1.02157540729928)*(-3.10521847114350*x + 1.01324631456330)*(-2.13082401398095*x + 1.00908971958995)*(-1.57606273371134*x + 1.00672320576998)*(-1.23155036189212*x + 1.00525357672762)*(-1.00428409891567*x + 1.00428409891567)*(-0.847828592283513*x + 1.00361668730671)*(-0.736932794743637*x + 1.00314362538478)*(-0.656958424493676*x + 1.00280246882038)*(-0.599006911254878*x + 1.00255525788147)*(-0.557490852972612*x + 1.00237815769591)*(-0.528849404638922*x + 1.00225597832667)*(-0.510840072448893*x + 1.00217915369050)*(-0.502142049457837*x + 1.00214204945784) + 0.947852670301149*(-15.0009709038443*x + 29.4292893916511)*(-9.94323556560999*x + 19.8440550412401)*(0.528849404638922*x - 0.00225597832666562)*(0.538506170611210*x - 0.0205571267105511)*(0.558557309966453*x - 0.0585573099664532)*(0.590604480144856*x - 0.119291930480371)*(0.637405937327926*x - 0.207988334115652)*(0.703435001162088*x - 0.333124192056695)*(0.795921724120067*x - 0.508401634344383)*(0.926858956070583*x - 0.756549069808644)*(1.11711461993291*x - 1.11711461993291)*(1.40565172786311*x - 1.66393955507599)*(1.87293406534249*x - 2.54951588776549)*(2.71200319899344*x - 4.13968890876986)*(4.51533219568122*x - 7.55729182552871)*(10.2937778233588*x - 18.5083898601943) + 0.0381650857052867*(-15.0009709038443*x + 1.57265241603751)*(-6.10469245155126*x + 1.23304270796572)*(-3.47065561255052*x + 1.13249004577776)*(-2.29677302315457*x + 1.08767783293695)*(-1.66504608567649*x + 1.06356206340831)*(-1.28522128800976*x + 1.04906249605037)*(-1.03968947708782*x + 1.03968947708782)*(-0.872923954755040*x + 1.03332331053181)*(-0.755819445409580*x + 1.02885292120599)*(-0.671926594931823*x + 1.02565036559660)*(-0.611425854288155*x + 1.02334078873496)*(-0.568232548933506*x + 1.02169191208381)*(-0.538506170611210*x + 1.02055712671055)*(-0.519844738543908*x + 1.01984473854391)*(-0.510840072448893*x + 1.01950099120729)*(29.4911017352397*x - 0.125803840867736) + 0.104644775394141*(-10.2937778233588*x + 2.07916578652318)*(-4.51533219568122*x + 1.47337256583374)*(-2.71200319899344*x + 1.28431748921701)*(-1.87293406534249*x + 1.19635224291949)*(-1.40565172786312*x + 1.14736390065024)*(-1.11711461993291*x + 1.11711461993291)*(-0.926858956070583*x + 1.09716884233252)*(-0.795921724120067*x + 1.08344181389575)*(-0.703435001162088*x + 1.07374581026748)*(-0.637405937327927*x + 1.06682354054020)*(-0.590604480144856*x + 1.06191702980934)*(-0.558557309966453*x + 1.05855730996645)*(-0.538506170611210*x + 1.05645521451187)*(-0.528849404638923*x + 1.05544283095118)*(9.94323556560997*x - 0.0424160899798354)*(15.0009709038443*x - 0.572652416037510) + 0.974296206412599*(-10.2937778233588*x + 19.5083898601943)*(-6.10469245155126*x + 11.9763421951368)*(-5.05773533823432*x + 10.0938952691693)*(0.557490852972612*x - 0.00237815769591202)*(0.568232548933506*x - 0.0216919120838062)*(0.590604480144856*x - 0.0619170298093412)*(0.626552889972155*x - 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0.233042707965716)*(10.2937778233588*x - 1.07916578652318) + 0.994710534957717*(-8.04365558072790*x + 14.4626313044576)*(-4.51533219568122*x + 8.55729182552871)*(-3.47065561255052*x + 6.80882117932328)*(-3.10521847114350*x + 6.19719062772370)*(0.599006911254878*x - 0.00255525788146924)*(0.611425854288155*x - 0.0233407887349600)*(0.637405937327927*x - 0.0668235405402013)*(0.679480365874805*x - 0.137243328308031)*(0.742174904521598*x - 0.242174904521598)*(0.833244588254671*x - 0.394597837453913)*(0.966242100365167*x - 0.617195194089080)*(1.16625534196685*x - 0.951956485229441)*(1.48434980904320*x - 1.48434980904320)*(2.04104073341934*x - 2.41608098402912)*(3.20047134023098*x - 4.35661493976025)*(6.79054980078360*x - 10.3653136195365) + 0.320544588125103*(-6.79054980078361*x + 3.21578598203069)*(-3.20047134023098*x + 2.04432774070171)*(-2.04104073341934*x + 1.66600048280956)*(-1.48434980904320*x + 1.48434980904320)*(-1.16625534196685*x + 1.38055419870426)*(-0.966242100365167*x + 1.31528900664125)*(-0.833244588254671*x + 1.27189133905543)*(-0.742174904521598*x + 1.24217490452160)*(-0.679480365874805*x + 1.22171740344158)*(-0.637405937327926*x + 1.20798833411565)*(-0.611425854288155*x + 1.19951091984135)*(-0.599006911254878*x + 1.19545856462829)*(3.10521847114350*x - 0.0132463145633008)*(3.47065561255052*x - 0.132490045777762)*(4.51533219568122*x - 0.473372565833740)*(8.04365558072791*x - 1.62467985699820) + 0.999016071874724*(-6.79054980078360*x + 11.3653136195365)*(-3.68208760742655*x + 6.62045695050802)*(-2.71200319899344*x + 5.13968890876986)*(-2.29677302315457*x + 4.50586821337219)*(-2.13082401398095*x + 4.25255830837195)*(0.656958424493676*x - 0.00280246882038193)*(0.671926594931823*x - 0.0256503655966001)*(0.703435001162088*x - 0.0737458102674813)*(0.755030737626759*x - 0.152503201874499)*(0.833244588254671*x - 0.271891339055430)*(0.949789992441032*x - 0.449789992441032)*(1.12653991506528*x - 0.719586759120762)*(1.40809039036728*x - 1.14935446009514)*(1.89957998488206*x - 1.89957998488206)*(2.91815186562080*x - 3.45436086384414)*(6.05361700603997*x - 8.24043569976073) + 0.978123653141135*(-6.05361700603997*x + 9.24043569976073)*(-3.20047134023098*x + 5.35661493976025)*(-2.28950538692543*x + 4.11657012764284)*(-1.87293406534249*x + 3.54951588776549)*(-1.66504608567649*x + 3.26653010794466)*(-1.57606273371134*x + 3.14540226165271)*(0.736932794743637*x - 0.00314362538478391)*(0.755819445409580*x - 0.0288529212059873)*(0.795921724120067*x - 0.0834418138957520)*(0.862620080497254*x - 0.174234395662578)*(0.966242100365167*x - 0.315289006641254)*(1.12653991506528*x - 0.533493071009790)*(1.38411497565444*x - 0.884114975654438)*(1.83489206679198*x - 1.49773153427350)*(2.76822995130888*x - 2.76822995130888)*(5.63405203655611*x - 6.66930638162676) + 0.456064366570132*(-6.05361700603996*x + 3.86679831231920)*(-2.91815186562080*x + 2.38194286739745)*(-1.89957998488206*x + 1.89957998488206)*(-1.40809039036728*x + 1.66682632063941)*(-1.12653991506528*x + 1.53349307100979)*(-0.949789992441032*x + 1.44978999244103)*(-0.833244588254671*x + 1.39459783745391)*(-0.755030737626759*x + 1.35755827337902)*(-0.703435001162088*x + 1.33312419205669)*(-0.671926594931823*x + 1.31820282426705)*(-0.656958424493676*x + 1.31111438016697)*(2.13082401398095*x - 0.00908971958994975)*(2.29677302315457*x - 0.0876778329369457)*(2.71200319899344*x - 0.284317489217014)*(3.68208760742655*x - 0.743718264345084)*(6.79054980078361*x - 2.21578598203069) + 0.596199046078406*(-5.63405203655611*x + 4.59879769148546)*(-2.76822995130888*x + 2.76822995130888)*(-1.83489206679198*x + 2.17205259931046)*(-1.38411497565444*x + 1.88411497565444)*(-1.12653991506528*x + 1.71958675912076)*(-0.966242100365167*x + 1.61719519408908)*(-0.862620080497254*x + 1.55100576533193)*(-0.795921724120067*x + 1.50840163434438)*(-0.755819445409581*x + 1.48278596961317)*(-0.736932794743637*x + 1.47072196410249)*(1.57606273371134*x - 0.00672320576997863)*(1.66504608567649*x - 0.0635620634083151)*(1.87293406534249*x - 0.196352242919489)*(2.28950538692543*x - 0.462440646208027)*(3.20047134023098*x - 1.04432774070171)*(6.05361700603996*x - 2.86679831231920) + 0.926027794020423*(-5.63405203655611*x + 7.66930638162676)*(-2.91815186562080*x + 4.45436086384414)*(-2.04104073341934*x + 3.41608098402912)*(-1.62795469238180*x + 2.92709058213418)*(-1.40565172786311*x + 2.66393955507599)*(-1.28522128800976*x + 2.52138007996914)*(-1.23155036189212*x + 2.45784714705662)*(0.847828592283513*x - 0.00361668730671057)*(0.872923954755040*x - 0.0333233105318129)*(0.926858956070583*x - 0.0971688423325229)*(1.01857188073873*x - 0.205733972685990)*(1.16625534196685*x - 0.380554198704257)*(1.40809039036728*x - 0.666826320639411)*(1.83489206679198*x - 1.17205259931046)*(2.72109557587590*x - 2.22109557587590)*(5.44219115175180*x - 5.44219115175180) + 0.728582695607967*(-5.44219115175180*x + 5.44219115175180)*(-2.72109557587590*x + 3.22109557587590)*(-1.83489206679198*x + 2.49773153427350)*(-1.40809039036728*x + 2.14935446009514)*(-1.16625534196685*x + 1.95195648522944)*(-1.01857188073873*x + 1.83140978879147)*(-0.926858956070583*x + 1.75654906980864)*(-0.872923954755040*x + 1.71252459897827)*(-0.847828592283513*x + 1.69204049726032)*(1.23155036189212*x - 0.00525357672761828)*(1.28522128800976*x - 0.0490624960503736)*(1.40565172786312*x - 0.147363900650239)*(1.62795469238180*x - 0.328818802629421)*(2.04104073341934*x - 0.666000482809556)*(2.91815186562080*x - 1.38194286739745)*(5.63405203655611*x - 3.59879769148546) + 0.841470984807897*(-5.44219115175180*x + 6.44219115175180)*(-2.76822995130888*x + 3.76822995130888)*(-1.89957998488206*x + 2.89957998488206)*(-1.48434980904320*x + 2.48434980904320)*(-1.25310577994431*x + 2.25310577994431)*(-1.11711461993291*x + 2.11711461993291)*(-1.03968947708782*x + 2.03968947708782)*(-1.00428409891567*x + 2.00428409891567)*(1.00428409891567*x - 0.00428409891567443)*(1.03968947708782*x - 0.0396894770878154)*(1.11711461993291*x - 0.117114619932907)*(1.25310577994431*x - 0.253105779944310)*(1.48434980904320*x - 0.484349809043196)*(1.89957998488206*x - 0.899579984882064)*(2.76822995130888*x - 1.76822995130888)*(5.44219115175180*x - 4.44219115175180) + 0.911064357137178*(0.502142049457837*x - 0.00214204945783722)*(0.510840072448893*x - 0.0195009912072870)*(0.528849404638923*x - 0.0554428309511795)*(0.557490852972612*x - 0.112603548249313)*(0.599006911254878*x - 0.195458564628287)*(0.656958424493676*x - 0.311114380166970)*(0.736932794743637*x - 0.470721964102491)*(0.847828592283513*x - 0.692040497260316)*(1.00428409891567*x - 1.00428409891567)*(1.23155036189212*x - 1.45784714705662)*(1.57606273371134*x - 2.14540226165271)*(2.13082401398095*x - 3.25255830837195)*(3.10521847114350*x - 5.19719062772370)*(5.05773533823432*x - 9.09389526916935)*(9.94323556560999*x - 18.8440550412401)*(29.4911017352398*x - 57.8563996296119) Der Fehler ist: Der Fehler ist: 1.58113883008419 None |
#Mit tschebyscheff Nullstellen wird das Interpolationpolynom immer genauer
PnTscheb2Mit2Stst=plot(pntscheb2(g,2),0,2,color='yellow')
PnTscheb2Mit8Stst=plot(pntscheb2(g,8),0,2,color='red')
PnTscheb2Mit16Stst=plot(pntscheb2(g,16),0,2,color='black')
PnTscheb2Mit32Stst=plot(pntscheb2(g,32),0,2,color='green')
PnTscheb2Mit64Stst=plot(pntscheb2(g,64),0,2,color='purple')
PnTscheb2Mit70Stst=plot(pntscheb2(g,70),0,2,color='purple')
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show(Funktion2+PnTscheb2Mit2Stst+PnTscheb2Mit8Stst+PnTscheb2Mit16Stst+PnTscheb2Mit32Stst+PnTscheb2Mit64Stst+PnTscheb2Mit70Stst)
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