elliptic_eu( z , m )

The incomplete elliptic integral of the second kind of a modified argument z and parameter m in SageMath. Defined by

\[ E(z|m) = \int_0^{ \sin[ \operatorname{sn}^{-1}z ] } du \sqrt{ 1 - m \sin^2 u } \]

Note that all elliptic integrals in SageMath use the parameter rather than the elliptic modulus k, which is related to the parameter by \( m = k^2 \).

Plot on the real axis:

Series expansion about the origin:

Special values:

Related functions:   elliptic_e   elliptic_ec

Function category: elliptic integrals sagemath-docs