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
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): elliptic integral