Weierstrass Elliptic and Modular Functions - 23.5 Special Lattices
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 23.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = i\eta_{3}}
\eta_{1} = i\eta_{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | eta[1] = I*eta[3] |
Subscript[\[Eta], 1] == I*Subscript[\[Eta], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 23.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = \tfrac{1}{2}}
k^{2} = \tfrac{1}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (k)^(2) = (1)/(2) |
(k)^(2) == Divide[1,2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 23.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \compellintKk'@{k}}
\compellintKk@{k} = \compellintKk'@{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | EllipticK(k) = diff( EllipticK(k), k$(1) )
|
EllipticK[(k)^2] == D[EllipticK[(k)^2], {k, 1}]
|
Failure | Failure | Error | Failed [3 / 3]
Result: Indeterminate
Test Values: {Rule[k, 1]}
Result: Complex[1.3320292471861073, -1.3934110303935494]
Test Values: {Rule[k, 2]}
... skip entries to safe data |
| 23.5#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk'@{k} = \ifrac{\left(\EulerGamma@{\tfrac{1}{4}}\right)^{2}}{\left(4\sqrt{\pi}\right)}}
\compellintKk'@{k} = \ifrac{\left(\EulerGamma@{\tfrac{1}{4}}\right)^{2}}{\left(4\sqrt{\pi}\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | diff( EllipticK(k), k$(1) ) = ((GAMMA((1)/(4)))^(2))/(4*sqrt(Pi))
|
D[EllipticK[(k)^2], {k, 1}] == Divide[(Gamma[Divide[1,4]])^(2),4*Sqrt[Pi]]
|
Failure | Failure | Error | Failed [3 / 3]
Result: Indeterminate
Test Values: {Rule[k, 1]}
Result: Complex[-2.343228747081181, 0.3151532066437278]
Test Values: {Rule[k, 2]}
... skip entries to safe data |
| 23.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{1} = e^{\pi i/3}\eta_{3}}
\eta_{1} = e^{\pi i/3}\eta_{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | eta[1] = exp(Pi*I/3)*eta[3] |
Subscript[\[Eta], 1] == Exp[Pi*I/3]*Subscript[\[Eta], 3] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 23.5#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = e^{\iunit\pi/3}}
k^{2} = e^{\iunit\pi/3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (k)^(2) = exp(I*Pi/3)
|
(k)^(2) == Exp[I*Pi/3]
|
Failure | Failure | Failed [3 / 3] Result: .5000000000-.8660254040*I
Test Values: {k = 1}
Result: 3.500000000-.8660254040*I
Test Values: {k = 2}
... skip entries to safe data |
Failed [3 / 3]
Result: Complex[0.4999999999999999, -0.8660254037844386]
Test Values: {Rule[k, 1]}
Result: Complex[3.5, -0.8660254037844386]
Test Values: {Rule[k, 2]}
... skip entries to safe data |
| 23.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = e^{\iunit\pi/6}\compellintKk'@{k}}
\compellintKk@{k} = e^{\iunit\pi/6}\compellintKk'@{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | EllipticK(k) = exp(I*Pi/6)*diff( EllipticK(k), k$(1) )
|
EllipticK[(k)^2] == Exp[I*Pi/6]*D[EllipticK[(k)^2], {k, 1}]
|
Failure | Failure | Error | Failed [3 / 3]
Result: Indeterminate
Test Values: {Rule[k, 1]}
Result: Complex[1.4240716315220228, -1.1066114718975122]
Test Values: {Rule[k, 2]}
... skip entries to safe data |
| 23.5#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e^{\iunit\pi/6}\compellintKk'@{k} = e^{\iunit\pi/12}\frac{3^{1/4}\left(\EulerGamma@{\frac{1}{3}}\right)^{3}}{2^{7/3}\pi}}
e^{\iunit\pi/6}\compellintKk'@{k} = e^{\iunit\pi/12}\frac{3^{1/4}\left(\EulerGamma@{\frac{1}{3}}\right)^{3}}{2^{7/3}\pi} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | exp(I*Pi/6)*diff( EllipticK(k), k$(1) ) = exp(I*Pi/12)*((3)^(1/4)*(GAMMA((1)/(3)))^(3))/((2)^(7/3)* Pi)
|
Exp[I*Pi/6]*D[EllipticK[(k)^2], {k, 1}] == Exp[I*Pi/12]*Divide[(3)^(1/4)*(Gamma[Divide[1,3]])^(3),(2)^(7/3)* Pi]
|
Failure | Failure | Error | Failed [3 / 3]
Result: Indeterminate
Test Values: {Rule[k, 1]}
Result: Complex[-2.1248830880335463, -0.38527593877730804]
Test Values: {Rule[k, 2]}
... skip entries to safe data |