Formula:6830

Digital Library of Mathematical Functions ID 19.5.E5

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle q=\exp@{-\pi\ccompellintKk@{k}/\compellintKk@{k}}=r+8r^{2}+84r^{3}+992r^{4}+\cdots,}

Constraint(s)

${\displaystyle{\displaystyle 0\leq k\leq 1}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}$: Legendre’s complementary complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle q}}$: nome
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
 

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