Weierstrass Elliptic and Modular Functions - 23.17 Elementary Properties
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 23.17#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{i} = \tfrac{1}{2}}
\modularlambdatau@{i} = \tfrac{1}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ModularLambda[I] == Divide[1,2]
|
Missing Macro Error | Successful | - | Successful [Tested: 1] |
| 23.17#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \KleincompinvarJtau@{i} = 1}
\KleincompinvarJtau@{i} = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
KleinInvariantJ[I] == 1
|
Missing Macro Error | Successful | - | Successful [Tested: 1] |
| 23.17#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{i} = \frac{\EulerGamma@{\tfrac{1}{4}}}{2\pi^{3/4}}}
\Dedekindeta@{i} = \frac{\EulerGamma@{\tfrac{1}{4}}}{2\pi^{3/4}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
DedekindEta[I] == Divide[Gamma[Divide[1,4]],2*(Pi)^(3/4)]
|
Missing Macro Error | Successful | - | Successful [Tested: 1] |
| 23.17.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\tau} = \sum_{n=-\infty}^{\infty}(-1)^{n}q^{(6n+1)^{2}/12}}
\Dedekindeta@{\tau} = \sum_{n=-\infty}^{\infty}(-1)^{n}q^{(6n+1)^{2}/12} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
DedekindEta[\[Tau]] == Sum[(- 1)^(n)* (q)^((6*n + 1)^(2)/12), {n, - Infinity, Infinity}, GenerateConditions->None]
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Missing Macro Error | Failure | - | Failed [10 / 10]
Result: Plus[0.7682254223260567, Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[Rational[1, 12], Power[Plus[1, Times[6, n]], 2]]]]
Test Values: {n, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Complex[0, 1]]}
Result: Plus[0.7682254223260567, Times[-1.0, NSum[Times[Power[-1, n], Power[Power[E, Times[Complex[0, Rational[2, 3]], Pi]], Times[Rational[1, 12], Power[Plus[1, Times[6, n]], 2]]]]
Test Values: {n, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Complex[0, 1]]}
... skip entries to safe data |
| 23.17.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modularlambdatau@{\tau} = 16q\prod_{n=1}^{\infty}\left(\frac{1+q^{2n}}{1+q^{2n-1}}\right)^{8}}
\modularlambdatau@{\tau} = 16q\prod_{n=1}^{\infty}\left(\frac{1+q^{2n}}{1+q^{2n-1}}\right)^{8} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
ModularLambda[\[Tau]] == 16*q*Product[(Divide[1 + (q)^(2*n),1 + (q)^(2*n - 1)])^(8), {n, 1, Infinity}, GenerateConditions->None]
|
Missing Macro Error | Failure | - | Failed [24 / 100]
Result: Indeterminate
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Indeterminate
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 23.17.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Dedekindeta@{\tau} = q^{1/12}\prod_{n=1}^{\infty}(1-q^{2n})}
\Dedekindeta@{\tau} = q^{1/12}\prod_{n=1}^{\infty}(1-q^{2n}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
DedekindEta[\[Tau]] == (q)^(1/12)* Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None]
|
Missing Macro Error | Failure | - | Failed [4 / 10]
Result: DirectedInfinity[]
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[τ, Complex[0, 1]]}
Result: DirectedInfinity[]
Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[τ, Complex[0, 1]]}
... skip entries to safe data |