Module « scipy.special »

Fonction eval_sh_jacobi - module scipy.special

Signature de la fonction eval_sh_jacobi

Description

eval_sh_jacobi.__doc__

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

eval_sh_jacobi(n, p, q, x, out=None)

Evaluate shifted Jacobi polynomial at a point.

Defined by

.. math::

    G_n^{(p, q)}(x)
      = \binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),

where :math:`P_n^{(\cdot, \cdot)}` is the n-th Jacobi
polynomial. See 22.5.2 in [AS]_ for details.

Parameters
----------
n : int
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to `binom` and `eval_jacobi`.
p : float
    Parameter
q : float
    Parameter

Returns
-------
G : ndarray
    Values of the shifted Jacobi polynomial.

See Also
--------
roots_sh_jacobi : roots and quadrature weights of shifted Jacobi
                  polynomials
sh_jacobi : shifted Jacobi polynomial object
eval_jacobi : evaluate Jacobi polynomials

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