Formula:7204

Digital Library of Mathematical Functions ID 19.25.E4

${\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=-\tfrac{1}{3}(k^{2}/\alpha^{2})R_{J}\left(0,1-k^{2},1,1-(k^{2}/\alpha^{2})\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-\infty<k^{2}<1<\alpha^{2}}}$

Symbols List

• ${\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}\right)}}$: symmetric elliptic integral of third kind
• ${\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the third kind
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle\alpha^{2}}}$: real or complex parameter
 

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