elliptic_f( z , m )
The incomplete elliptic integral of the first kind of z and parameter m in SageMath. Defined by
\[ F(z|m) = \int_0^z \frac{ du }{ \sqrt{ 1 - m \sin^2 u } } \]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_kc elliptic_e elliptic_pi
Function category: elliptic integrals sagemath-docs