Formula:6834

Digital Library of Mathematical Functions ID 19.5.E9

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \compellintEk@{k}=\compellintKk@{k}+\frac{2\pi^{2}}{\compellintKk@{k}}\,\frac{\sum_{n=1}^{\infty}(-1)^{n}n^{2}q^{n^{2}}}{1+2\sum_{n=1}^{\infty}(-1)^{n}q^{n^{2}}},}

Constraint(s)

${\displaystyle{\displaystyle|q|<1}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle E\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the second kind
• ${\displaystyle{\displaystyle q}}$: nome
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
 

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