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