# mars.tensor.special.ellipkm1#

mars.tensor.special.ellipkm1(x, **kwargs)[source]#

Complete elliptic integral of the first kind around m = 1

This function is defined as

$K(p) = \int_0^{\pi/2} [1 - m \sin(t)^2]^{-1/2} dt$

where m = 1 - p.

Parameters

p (array_like) – Defines the parameter of the elliptic integral as m = 1 - p.

Returns

K – Value of the elliptic integral.

Return type

ndarray

Notes

Wrapper for the Cephes 1 routine ellpk.

For p <= 1, computation uses the approximation,

$K(p) \approx P(p) - \log(p) Q(p),$

where $$P$$ and $$Q$$ are tenth-order polynomials. The argument p is used internally rather than m so that the logarithmic singularity at m = 1 will be shifted to the origin; this preserves maximum accuracy. For p > 1, the identity

$K(p) = K(1/p)/\sqrt(p)$

is used.

ellipk

Complete elliptic integral of the first kind

ellipkinc

Incomplete elliptic integral of the first kind

ellipe

Complete elliptic integral of the second kind

ellipeinc

Incomplete elliptic integral of the second kind

References

1

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/