Functions of Number Theory - 27.13 Functions
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 27.13.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}}
\AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x| < 1} | 1+2*(sum((x)^(m^2), m = 1 .. infinity)) = 1 + 2*sum((x)^((m)^(2)), m = 1..infinity)
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Error
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Successful | Missing Macro Error | - | - |
| 27.13.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}}
(\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |x| < 1} | (1+2*(sum((x)^(m^2), m = 1 .. infinity)))^(2) = 1 + 4*sum((delta[1](n)- delta[3](n))*(x)^(n), n = 1..infinity)
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Error
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Failure | Missing Macro Error | Failed [300 / 300] Result: 3.532372013
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = 1/2*3^(1/2)+1/2*I}
Result: -7.395831219+2.928203232*I
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
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