Formula:7312

Digital Library of Mathematical Functions ID 19.28.E8

${\displaystyle{\displaystyle\int_{0}^{\infty}R_{J}\left(tx,y,z,tp\right)\mathrm{d}t=\frac{6}{\sqrt{p}}R_{C}\left(p,x\right)R_{F}\left(0,y,z\right).}}$

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
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
 

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