Formula:7126

Digital Library of Mathematical Functions ID 19.21.E12

${\displaystyle{\displaystyle(p-x)R_{J}\left(x,y,z,p\right)+(q-x)R_{J}\left(x,y,z,q\right)=3R_{F}\left(x,y,z\right)-3R_{C}\left(\xi,\eta\right),}}$

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
• ${\displaystyle{\displaystyle\xi}}$: ξ
• ${\displaystyle{\displaystyle\eta}}$: η
 

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