Formula:7174

Digital Library of Mathematical Functions ID 19.23.E7

${\displaystyle{\displaystyle R_{G}\left(x,y,z\right)=\frac{1}{4}\int_{0}^{\infty}\frac{1}{\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}}\*\left(\frac{x}{t+x}+\frac{y}{t+y}+\frac{z}{t+z}\right)t\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle x,y,z\in\mathbb{C}\setminus(-\infty,0]}}$

Symbols List

• ${\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of second kind
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$:
• ${\displaystyle{\displaystyle\setminus}}$:
 

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