Formula:7311

Digital Library of Mathematical Functions ID 19.28.E7

${\displaystyle{\displaystyle\int_{0}^{\infty}R_{J}\left(x,y,z,r^{2}\right)\mathrm{d}r=\tfrac{3}{2}\pi R_{F}\left(xy,xz,yz\right),}}$

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
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
 

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