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Module « scipy.special »

Fonction lpmn - module scipy.special

Signature de la fonction lpmn

def lpmn(m, n, z) 

Description

help(scipy.special.lpmn)

Sequence of associated Legendre functions of the first kind.

Computes the associated Legendre function of the first kind of order m and
degree n, ``Pmn(z)`` = :math:`P_n^m(z)`, and its derivative, ``Pmn'(z)``.
Returns two arrays of size ``(m+1, n+1)`` containing ``Pmn(z)`` and
``Pmn'(z)`` for all orders from ``0..m`` and degrees from ``0..n``.

This function takes a real argument ``z``. For complex arguments ``z``
use clpmn instead.

.. deprecated:: 1.15.0
    This function is deprecated and will be removed in SciPy 1.17.0.
    Please `scipy.special.assoc_legendre_p_all` instead.

Parameters
----------
m : int
   ``|m| <= n``; the order of the Legendre function.
n : int
   where ``n >= 0``; the degree of the Legendre function.  Often
   called ``l`` (lower case L) in descriptions of the associated
   Legendre function
z : array_like
    Input value.

Returns
-------
Pmn_z : (m+1, n+1) array
   Values for all orders 0..m and degrees 0..n
Pmn_d_z : (m+1, n+1) array
   Derivatives for all orders 0..m and degrees 0..n

See Also
--------
clpmn: associated Legendre functions of the first kind for complex z

Notes
-----
In the interval (-1, 1), Ferrer's function of the first kind is
returned. The phase convention used for the intervals (1, inf)
and (-inf, -1) is such that the result is always real.

References
----------
.. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
       Functions", John Wiley and Sons, 1996.
       https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
.. [2] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/14.3

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