Formula:7275

Digital Library of Mathematical Functions ID 19.26.E22

${\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=2R_{J}\left(x+\lambda,y+\lambda,z+\lambda,p+\lambda\right)+3R_{C}\left(\alpha^{2},\beta^{2}\right),}}$

Symbols List

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

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