Module « scipy.special »

Fonction ellipkm1 - module scipy.special

Signature de la fonction ellipkm1

Description

ellipkm1.__doc__

ellipkm1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

ellipkm1(p)

Complete elliptic integral of the first kind around `m` = 1

This function is defined as

.. math:: 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 : ndarray
    Value of the elliptic integral.

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

For `p <= 1`, computation uses the approximation,

.. math:: K(p) \approx P(p) - \log(p) Q(p),

where :math:`P` and :math:`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

.. math:: K(p) = K(1/p)/\sqrt(p)

is used.

See Also
--------
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/