Definition:Elliptic Integral of the Second Kind/Complete/Definition 2

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

• Equivalence of Definitions of Elliptic Integral of the Second Kind

• Definition:Incomplete Elliptic Integral of the First Kind
• Definition:Complete Elliptic Integral of the First Kind

• Definition:Incomplete Elliptic Integral of the Second 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