Symbols:E/Complete Elliptic Integral of the Second Kind

Complete Elliptic Integral of the Second Kind

$\map E k$

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

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

The $\LaTeX$ code for \(\map E k\) is \map E k .

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): E: 3.