Theta Functions - 20.8 Watson’s Expansions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 20.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{3}@{z}{q}\Jacobithetaq{4}@{z}{q}}{\Jacobithetaq{2}@{z}{q}} = 2\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}q^{n^{2}}e^{i2nz}}{q^{-n}e^{-iz}+q^{n}e^{iz}}}
\frac{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{3}@{z}{q}\Jacobithetaq{4}@{z}{q}}{\Jacobithetaq{2}@{z}{q}} = 2\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}q^{n^{2}}e^{i2nz}}{q^{-n}e^{-iz}+q^{n}e^{iz}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (JacobiTheta2(0, q)*JacobiTheta3(z, q)*JacobiTheta4(z, q))/(JacobiTheta2(z, q)) = 2*sum(((- 1)^(n)* (q)^((n)^(2))* exp(I*2*n*z))/((q)^(- n)* exp(- I*z)+ (q)^(n)* exp(I*z)), n = - infinity..infinity)
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Divide[EllipticTheta[2, 0, q]*EllipticTheta[3, z, q]*EllipticTheta[4, z, q],EllipticTheta[2, z, q]] == 2*Sum[Divide[(- 1)^(n)* (q)^((n)^(2))* Exp[I*2*n*z],(q)^(- n)* Exp[- I*z]+ (q)^(n)* Exp[I*z]], {n, - Infinity, Infinity}, GenerateConditions->None]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |