Definition:Complete Elliptic Integral of the Second Kind/Definition 1

Special Function

$\ds \map E k = \int \limits_0^{\pi / 2} \sqrt {1 - k^2 \sin^2 \phi} \rd \phi$

is the complete elliptic integral of the second kind, and is a function of $k$, defined on the interval $0 < k < 1$.

Also see

• Equivalence of Definitions of Complete Elliptic Integral of the Second Kind

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $34.4$: Complete Elliptic Integral of the Second Kind
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): elliptic integral