Formula:7257

Digital Library of Mathematical Functions ID 19.26.E9

${\displaystyle{\displaystyle R_{J}\left(x+\lambda,y+\lambda,z+\lambda,p+\lambda\right)+R_{J}\left(x+\mu,y+\mu,z+\mu,p+\mu\right)=R_{J}\left(x,y,z,p\right)-3R_{C}\left(\gamma-\delta,\gamma\right),}}$

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
• ${\displaystyle{\displaystyle\delta}}$: δ
• ${\displaystyle{\displaystyle x}}$: positive
• ${\displaystyle{\displaystyle y}}$: positive
• ${\displaystyle{\displaystyle z}}$: positive
• ${\displaystyle{\displaystyle\mu>0}}$: parameter
• ${\displaystyle{\displaystyle\gamma}}$: γ
 

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