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scipy.special.ellipk

scipy.special.ellipk(m)

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 : array_like

Value of the elliptic integral.

See also

ellipkm1

Complete elliptic integral of the first kind around m = 1

ellipkinc

Incomplete elliptic integral of the first kind

ellipe

Complete elliptic integral of the second kind

ellipeinc

Incomplete elliptic integral of the second kind

Notes

For more precision around point m = 1, use ellipkm1, which this function calls.