Module « scipy.special »

Fonction lpmv - module scipy.special

Signature de la fonction lpmv

Description

lpmv.__doc__

lpmv(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

lpmv(m, v, x)

Associated Legendre function of integer order and real degree.

Defined as

.. math::

    P_v^m = (-1)^m (1 - x^2)^{m/2} \frac{d^m}{dx^m} P_v(x)

where

.. math::

    P_v = \sum_{k = 0}^\infty \frac{(-v)_k (v + 1)_k}{(k!)^2}
            \left(\frac{1 - x}{2}\right)^k

is the Legendre function of the first kind. Here :math:`(\cdot)_k`
is the Pochhammer symbol; see `poch`.

Parameters
----------
m : array_like
    Order (int or float). If passed a float not equal to an
    integer the function returns NaN.
v : array_like
    Degree (float).
x : array_like
    Argument (float). Must have ``|x| <= 1``.

Returns
-------
pmv : ndarray
    Value of the associated Legendre function.

See Also
--------
lpmn : Compute the associated Legendre function for all orders
       ``0, ..., m`` and degrees ``0, ..., n``.
clpmn : Compute the associated Legendre function at complex
        arguments.

Notes
-----
Note that this implementation includes the Condon-Shortley phase.

References
----------
.. [1] Zhang, Jin, "Computation of Special Functions", John Wiley
       and Sons, Inc, 1996.