Formula:7314

Digital Library of Mathematical Functions ID 19.28.E10

${\displaystyle{\displaystyle\int_{0}^{\infty}R_{F}\left((ac+bd)^{2},(ad+bc)^{2},4abcd{\cosh^{2}}z\right)\mathrm{d}z=\tfrac{1}{2}R_{F}\left(0,a^{2},b^{2}\right)R_{F}\left(0,c^{2},d^{2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle a,b,c,d>0}}$

Symbols List

• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of first kind
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\int}}$: integral
 

Resources that cite this formula

No records found.