maxframe.tensor.special.ellipkinc#
- maxframe.tensor.special.ellipkinc(phi, m, out=None)[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
out (ndarray, optional) – Optional output array for the function values
- Returns:
K – Value of the elliptic integral
- Return type:
scalar or ndarray
See also
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.
The Legendre K incomplete integral (or F integral) is related to Carlson’s symmetric R_F function [3]. Setting \(c = \csc^2\phi\),
\[F(\phi, m) = R_F(c-1, c-k^2, c) .\]References