# mars.tensor.special.ellipkinc#

mars.tensor.special.ellipkinc(phi, m, **kwargs)[source]#

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 – Value of the elliptic integral

Return type

ndarray

Notes

Wrapper for the Cephes 1 routine ellik. The computation is carried out using the arithmetic-geometric mean algorithm.

The parameterization in terms of $$m$$ follows that of section 17.2 in 2. Other parameterizations in terms of the complementary parameter $$1 - m$$, modular angle $$\sin^2(\alpha) = m$$, or modulus $$k^2 = m$$ are also used, so be careful that you choose the correct parameter.

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

References

1

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

2

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.