Formula:7119

Digital Library of Mathematical Functions ID 19.21.E5

${\displaystyle{\displaystyle 2R_{G}\left(0,z-1,z\right)=2R_{G}\left(0,1-z,1\right)\pm\mathrm{i}2R_{G}\left(0,z,1\right)+(z-1)R_{F}\left(0,1-z,1\right)\mp\mathrm{i}zR_{F}\left(0,z,1\right).}}$

Symbols List

• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of first kind
• ${\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of second kind
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
 

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