Weierstrass Elliptic and Modular Functions - 23.11 Integral Representations
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 23.11#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{1}(s,\tau) = \frac{\cosh^{2}@{\tfrac{1}{2}\tau s}}{1-2e^{-s}\cosh@{\tau s}+e^{-2s}}}
f_{1}(s,\tau) = \frac{\cosh^{2}@{\tfrac{1}{2}\tau s}}{1-2e^{-s}\cosh@{\tau s}+e^{-2s}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | f[1](s , tau) = ((cosh((1)/(2)*tau*s))^(2))/(1 - 2*exp(- s)*cosh(tau*s)+ exp(- 2*s))
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Subscript[f, 1][s , \[Tau]] == Divide[(Cosh[Divide[1,2]*\[Tau]*s])^(2),1 - 2*Exp[- s]*Cosh[\[Tau]*s]+ Exp[- 2*s]]
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Failure | Failure | Failed [300 / 300] Result: (.8660254040+.5000000000*I)*(-1.500000000, .8660254040+.5000000000*I)-.2283852288e-1-.9974318068e-1*I
Test Values: {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I}
Result: (-.5000000000+.8660254040*I)*(-1.500000000, .8660254040+.5000000000*I)-.2283852288e-1-.9974318068e-1*I
Test Values: {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[1] = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Error |
| 23.11#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{2}(s,\tau) = \frac{\cos^{2}@{\tfrac{1}{2}s}}{1-2e^{i\tau s}\cos@@{s}+e^{2i\tau s}}}
f_{2}(s,\tau) = \frac{\cos^{2}@{\tfrac{1}{2}s}}{1-2e^{i\tau s}\cos@@{s}+e^{2i\tau s}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | f[2](s , tau) = ((cos((1)/(2)*s))^(2))/(1 - 2*exp(I*tau*s)*cos(s)+ exp(2*I*tau*s))
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Subscript[f, 2][s , \[Tau]] == Divide[(Cos[Divide[1,2]*s])^(2),1 - 2*Exp[I*\[Tau]*s]*Cos[s]+ Exp[2*I*\[Tau]*s]]
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Failure | Failure | Failed [300 / 300] Result: (.8660254040+.5000000000*I)*(-1.500000000, .8660254040+.5000000000*I)+.1236929557-.8606824183e-1*I
Test Values: {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I}
Result: (-.5000000000+.8660254040*I)*(-1.500000000, .8660254040+.5000000000*I)+.1236929557-.8606824183e-1*I
Test Values: {s = -3/2, tau = 1/2*3^(1/2)+1/2*I, f[2] = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Error |