Formula:7115

Digital Library of Mathematical Functions ID 19.21.E1

${\displaystyle{\displaystyle R_{F}\left(0,z+1,z\right)R_{D}\left(0,z+1,1\right)+R_{D}\left(0,z+1,z\right)R_{F}\left(0,z+1,1\right)=3\pi/(2z),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: elliptic integral symmetric in only two variables
• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$:
• ${\displaystyle{\displaystyle\setminus}}$:
 

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