elliptic_ec( z , m )
The complete elliptic integral of the second kind of parameter m in SageMath. Defined by
\[ E(m) = \int_0^{ \frac{\pi}{2} } du \sqrt{ 1 - m \sin^2 u } = E \left( \frac{\pi}{2} \middle| m \right) \]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_eu
Function category: elliptic integrals sagemath-docs