mars.tensor.special.ellipeinc#

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

Incomplete elliptic integral of the second kind

This function is defined as

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

Parameters

phi (array_like) – amplitude of the elliptic integral.
m (array_like) – parameter of the elliptic integral.

Returns

E – Value of the elliptic integral.

Return type

ndarray

Notes

Wrapper for the Cephes 1 routine ellie.

Computation uses arithmetic-geometric means 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.