Weierstrass Elliptic and Modular Functions - 23.6 Relations to Other Functions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 23.6#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = e^{i\pi\tau}}
q = e^{i\pi\tau} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q = exp(I*Pi*tau) |
q == Exp[I*Pi*\[Tau]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 23.6#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = \omega_{3}/\omega_{1}}
\tau = \omega_{3}/\omega_{1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tau = omega[3]/omega[1] |
\[Tau] == Subscript[\[Omega], 3]/Subscript[\[Omega], 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 23.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = -\frac{\pi^{2}}{12\omega_{1}}\frac{\Jacobithetaq{1}'''@{0}{q}}{\Jacobithetaq{1}'@{0}{q}}}
\eta_{1} = -\frac{\pi^{2}}{12\omega_{1}}\frac{\Jacobithetaq{1}'''@{0}{q}}{\Jacobithetaq{1}'@{0}{q}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | eta[1] = -((Pi)^(2))/(12*omega[1])*(diff( JacobiTheta1(0, q), 0$(3) ))/(diff( JacobiTheta1(0, q), 0$(1) ))
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Subscript[\[Eta], 1] == -Divide[(Pi)^(2),12*Subscript[\[Omega], 1]]*Divide[D[EllipticTheta[1, 0, q], {0, 3}],D[EllipticTheta[1, 0, q], {0, 1}]]
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Error | Failure | - | Failed [300 / 300]
Result: Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[0.712277344720507, -0.4112335167120565], Power[D[0.0
Test Values: {0.0, 1.0}], -1], D[0.0, {0.0, 3.0}]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[Complex[-0.4112335167120564, -0.712277344720507], Power[D[0.0
Test Values: {0.0, 1.0}], -1], D[0.0, {0.0, 3.0}]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ω, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 23.6#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk^{2}@@{k} = (\compellintKk@{k})^{2}}
\compellintKk^{2}@@{k} = (\compellintKk@{k})^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (EllipticK(k))^(2) = (EllipticK(k))^(2)
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(EllipticK[(k)^2])^(2) == (EllipticK[(k)^2])^(2)
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Successful | Successful | - | Successful [Tested: 3] |