Definition:Complete Elliptic Integral of the First Kind/Definition 2
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Special Function
- $\ds \map K k = \int \limits_0^1 \frac {\d v} {\sqrt {\paren {1 - v^2} \paren {1 - k^2 v^2} } }$
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