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.