Jacobian Elliptic Functions - 22.17 Moduli Outside the Interval [0,1]
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 22.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}}
\genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k
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genJacobiellk[p]*q* z*k == genJacobiellk[p]*q* z- k
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Failure | Failure | Error | Failed [300 / 300]
Result: 1.0
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[2.0, Times[Complex[0.0, 1.0], genJacobiellk]]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 22.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}}
\Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | JacobiSN(z, 1/k) = k*JacobiSN(z/k, k)
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JacobiSN[z, (1/k)^2] == k*JacobiSN[z/k, (k)^2]
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Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.17.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}}
\Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | JacobiCN(z, 1/k) = JacobiDN(z/k, k)
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JacobiCN[z, (1/k)^2] == JacobiDN[z/k, (k)^2]
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Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.17.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}}
\Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | JacobiDN(z, 1/k) = JacobiCN(z/k, k)
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JacobiDN[z, (1/k)^2] == JacobiCN[z/k, (k)^2]
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Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |