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): $\S 34$: Elliptic Functions: Complete Elliptic Integral of the Second Kind: $34.4$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): elliptic integral
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 35$: Elliptic Functions: Complete Elliptic Integral of the Second Kind: $35.4.$