maxframe.tensor.special.ellipk#
- maxframe.tensor.special.ellipk(m, out=None)[source]#
Complete elliptic integral of the first kind.
This function is defined as
\[K(m) = \int_0^{\pi/2} [1 - m \sin(t)^2]^{-1/2} dt\]- Parameters:
m (array_like) – The 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
For more precision around point m = 1, use ellipkm1, which this function calls.
The parameterization in terms of \(m\) follows that of section 17.2 in [1]. 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 integral is related to Carlson’s symmetric R_F function by [2]:
\[K(m) = R_F(0, 1-k^2, 1) .\]References