Module « scipy.special »

Fonction ellipk - module scipy.special

Signature de la fonction ellipk

Description

ellipk.__doc__

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

ellipk(m)

Complete elliptic integral of the first kind.

This function is defined as

.. math:: 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.

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

The parameterization in terms of :math:`m` follows that of section
17.2 in [1]_. 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 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

References
----------
.. [1] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.