Definition:Complete Elliptic Integral of the Third Kind/Definition 2
< Definition:Complete Elliptic Integral of the Third Kind(Redirected from Definition:Elliptic Integral of the Third Kind/Complete/Definition 2)
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Special Function
- $\ds \map \Pi {k, n} = \int \limits_0^1 \frac {\d v} {\paren {1 + n v^2} \sqrt {\paren {1 - v^2} \paren {1 - k^2 v^2} } }$
is the complete elliptic integral of the third kind, and is a function of the variables:
- $k$, defined on the interval $0 < k < 1$
- $n \in \Z$
Also see
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $34.6$: Complete Elliptic Integral of the Third Kind