Definition:Incomplete Elliptic Integral of the Third Kind/Completion

Special Function

Let $\map \Pi {k, n, \dfrac \pi 2}$ denote the incomplete elliptic integral of the third kind.

Then:

$\map \Pi {k, n, \dfrac \pi 2} = \map \Pi {k, n}$

where $\map \Pi {k, n}$ denotes the complete elliptic integral of the third kind.