mars.tensor.special.ellipk#

mars.tensor.special.ellipk(x, **kwargs)[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.
Returns: K – Value of the elliptic integral.
Return type: array_like

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.