Formula:7222

Digital Library of Mathematical Functions ID 19.25.E22

${\displaystyle{\displaystyle\mathrm{el3}\left(x,k_{c},p\right)=\mathrm{el1}\left(x,k_{c}\right)+\tfrac{1}{3}{(1-p)}R_{J}\left(r,r+k_{c}^{2},r+1,r+p\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{el1}\left(\NVar{x},\NVar{k_{c}}\right)}}$: Bulirsch’s incomplete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\mathrm{el3}\left(\NVar{x},\NVar{k_{c}},\NVar{p}\right)}}$: Bulirsch’s incomplete elliptic integral of the third kind
• ${\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}\right)}}$: symmetric elliptic integral of third kind
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle r}}$: inverse
 

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