Formula:7152

Digital Library of Mathematical Functions ID 19.22.E14

${\displaystyle{\displaystyle R_{J}\left(0,g_{0}^{2},a_{0}^{2},-q_{0}^{2}\right)=\frac{-3\pi}{4M\left(a_{0},g_{0}\right)(q_{0}^{2}+a_{0}^{2})}\*\left(2+\frac{a_{0}^{2}-g_{0}^{2}}{q_{0}^{2}+g_{0}^{2}}\sum_{n=0}^{\infty}Q_{n}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}\right)}}$: symmetric elliptic integral of third kind
• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle Q_{n}}}$: modified parameter
• ${\displaystyle{\displaystyle a_{n}}}$: iterate
• ${\displaystyle{\displaystyle g_{n}}}$: iterate
 

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