SciPy

scipy.special.ellipkinc

scipy.special.ellipkinc(phi, m) = <ufunc 'ellipkinc'>

Incomplete elliptic integral of the first kind

This function is defined as

\[K(\phi, m) = \int_0^{\phi} [1 - m \sin(t)^2]^{-1/2} dt\]

This function is also called F(phi, m).

Parameters:

phi : array_like

amplitude of the elliptic integral

m : array_like

parameter of the elliptic integral

Returns:

K : ndarray

Value of the elliptic integral

See also

ellipkm1
Complete elliptic integral of the first kind, near m = 1
ellipk
Complete elliptic integral of the first kind
ellipe
Complete elliptic integral of the second kind
ellipeinc
Incomplete elliptic integral of the second kind

Notes

Wrapper for the Cephes [R318] routine ellik. The computation is carried out using the arithmetic-geometric mean algorithm.

References

[R318](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

Previous topic

scipy.special.ellipkm1

Next topic

scipy.special.ellipe