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Fonction eval_gegenbauer - module scipy.special

Signature de la fonction eval_gegenbauer

Description

eval_gegenbauer.__doc__

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

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

Evaluate Gegenbauer polynomial at a point.

The Gegenbauer polynomials can be defined via the Gauss
hypergeometric function :math:`{}_2F_1` as

.. math::

    C_n^{(\alpha)} = \frac{(2\alpha)_n}{\Gamma(n + 1)}
      {}_2F_1(-n, 2\alpha + n; \alpha + 1/2; (1 - z)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.46 in [AS]_ for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the Gauss hypergeometric
    function.
alpha : array_like
    Parameter
x : array_like
    Points at which to evaluate the Gegenbauer polynomial

Returns
-------
C : ndarray
    Values of the Gegenbauer polynomial

See Also
--------
roots_gegenbauer : roots and quadrature weights of Gegenbauer
                   polynomials
gegenbauer : Gegenbauer polynomial object
hyp2f1 : Gauss hypergeometric function

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