Formula:7202

Digital Library of Mathematical Functions ID 19.25.E2

${\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)-K\left(k\right)=\tfrac{1}{3}\alpha^{2}R_{J}\left(0,{k^{\prime}}^{2},1,1-\alpha^{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}\right)}}$: symmetric elliptic integral of third kind
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the third kind
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
• ${\displaystyle{\displaystyle\alpha^{2}}}$: real or complex parameter
 

Resources that cite this formula

No records found.