Module « scipy.special »

Fonction ellipeinc - module scipy.special

Signature de la fonction ellipeinc

Description

ellipeinc.__doc__

ellipeinc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

ellipeinc(phi, m)

Incomplete elliptic integral of the second kind

This function is defined as

.. math:: 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.

Notes
-----
Wrapper for the Cephes [1]_ routine `ellie`.

Computation uses arithmetic-geometric means algorithm.

The parameterization in terms of :math:`m` follows that of section
17.2 in [2]_. Other parameterizations in terms of the
complementary parameter :math:`1 - m`, modular angle
:math:`\sin^2(\alpha) = m`, or modulus :math:`k^2 = m` are also
used, so be careful that you choose the correct parameter.

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

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/
.. [2] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.