Formula:7141

Digital Library of Mathematical Functions ID 19.22.E7

${\displaystyle{\displaystyle 2p^{2}R_{J}\left(0,x^{2},y^{2},p^{2}\right)=v_{+}v_{-}R_{J}\left(0,xy,a^{2},v^{2}_{+}\right)+3R_{F}\left(0,xy,a^{2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle v_{\pm}=(p^{2}\pm xy)/(2p)}}$

Symbols List

• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: 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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