Module « scipy.special »

Fonction eval_genlaguerre - module scipy.special

Signature de la fonction eval_genlaguerre

Description

eval_genlaguerre.__doc__

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

eval_genlaguerre(n, alpha, x, out=None)

Evaluate generalized Laguerre polynomial at a point.

The generalized Laguerre polynomials can be defined via the
confluent hypergeometric function :math:`{}_1F_1` as

.. math::

    L_n^{(\alpha)}(x) = \binom{n + \alpha}{n}
      {}_1F_1(-n, \alpha + 1, x).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.54 in [AS]_ for details. The Laguerre
polynomials are the special case where :math:`\alpha = 0`.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the confluent hypergeometric
    function.
alpha : array_like
    Parameter; must have ``alpha > -1``
x : array_like
    Points at which to evaluate the generalized Laguerre
    polynomial

Returns
-------
L : ndarray
    Values of the generalized Laguerre polynomial

See Also
--------
roots_genlaguerre : roots and quadrature weights of generalized
                    Laguerre polynomials
genlaguerre : generalized Laguerre polynomial object
hyp1f1 : confluent hypergeometric function
eval_laguerre : evaluate Laguerre polynomials

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