Formula:7306

Digital Library of Mathematical Functions ID 19.28.E2

${\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}R_{G}\left(0,t,1\right)\mathrm{d}t=\frac{\sigma}{4\sigma+2}\left(\mathrm{B}\left(\sigma,\tfrac{1}{2}\right)\right)^{2},}}$

Symbols List

• ${\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of second kind
• ${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$: beta function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sigma}}$: parameter
 

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