Definition:Incomplete Elliptic Integral of the First Kind/Completion

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Special Function

Let $\map F {k, \dfrac \pi 2}$ denote the incomplete elliptic integral of the first kind.

Then:

$\map F {k, \dfrac \pi 2} = \map K k$

where $\map K k$ denotes the complete elliptic integral of the first kind.


Sources