Formula:7162

Digital Library of Mathematical Functions ID 19.22.E20

${\displaystyle{\displaystyle(p_{\pm}^{2}-p_{\mp}^{2})R_{J}\left(x^{2},y^{2},z^{2},p^{2}\right)=2(p_{\pm}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{\pm}^{2}\right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}$: Carlson’s combination of inverse circular and inverse hyperbolic functions
• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of first kind
• ${\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}\right)}}$: symmetric elliptic integral of third kind
 

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