Module « scipy.special »

Fonction eval_jacobi - module scipy.special

Signature de la fonction eval_jacobi

Description

eval_jacobi.__doc__

eval_jacobi(x1, x2, x3, x4, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

eval_jacobi(n, alpha, beta, x, out=None)

Evaluate Jacobi polynomial at a point.

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

.. math::

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

where :math:`(\cdot)_n` is the Pochhammer symbol; see `poch`. When
:math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.42 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
beta : array_like
    Parameter
x : array_like
    Points at which to evaluate the polynomial

Returns
-------
P : ndarray
    Values of the Jacobi polynomial

See Also
--------
roots_jacobi : roots and quadrature weights of Jacobi polynomials
jacobi : Jacobi 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.