# 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 K : ndarray Value of the elliptic integral

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 [R347] routine ellik. The computation is carried out using the arithmetic-geometric mean algorithm.

References

 [R347] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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