SciPy

scipy.special.ellipeinc

scipy.special.ellipeinc(phi, m) = <ufunc 'ellipeinc'>

Incomplete elliptic integral of the second kind

This function is defined as

\[E(\phi, m) = \int_0^{\phi} [1 - m \sin(t)^2]^{1/2} dt\]
Parameters:

phi : array_like

amplitude of the elliptic integral.

m : array_like

parameter of the elliptic integral.

Returns:

E : ndarray

Value of the elliptic integral.

See also

ellipkm1
Complete elliptic integral of the first kind, near m = 1
ellipk
Complete elliptic integral of the first kind
ellipkinc
Incomplete elliptic integral of the first kind
ellipe
Complete elliptic integral of the second kind

Notes

Wrapper for the Cephes [R329] routine ellie.

Computation uses arithmetic-geometric means algorithm.

References

[R329](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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