Definition:Complete Elliptic Integral of the First Kind/Definition 1
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Special Function
- $\ds \map K k = \int \limits_0^{\pi / 2} \frac {\d \phi} {\sqrt {1 - k^2 \sin^2 \phi} }$
is the complete elliptic integral of the first kind, and is a function of $k$, defined on the interval $0 < k < 1$.
Also see
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $34.2$: Complete Elliptic Integral of the First Kind
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): elliptic integral