Formula:6842

Digital Library of Mathematical Functions ID 19.6.E3

${\displaystyle{\displaystyle\Pi\left(\alpha^{2},0\right)=\pi/(2\sqrt{1-\alpha^{2}}),\quad\Pi\left(0,k\right)=K\left(k\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-\infty<\alpha^{2}<1}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: 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
• ${\displaystyle{\displaystyle\alpha^{2}}}$: real or complex parameter
 

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