Definition:Elliptic Integral of the Second Kind/Complete/Definition 2
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Special Function
- $\displaystyle E \left({k}\right) = \int \limits_0^1 \dfrac {\sqrt{1 - k^2 v^2} } {\sqrt{1 - v^2}} \, \mathrm d v$
is the complete elliptic integral of the second kind, and is a function of $k$, defined on the interval $0 < k < 1$.
Also see
- Definition:Incomplete Elliptic Integral of the First Kind
- Definition:Complete Elliptic Integral of the First Kind
- Definition:Incomplete Elliptic Integral of the Third Kind
- Definition:Complete Elliptic Integral of the Third Kind
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $34.4$: Complete Elliptic Integral of the Second Kind