Module « scipy.special »

Fonction sh_jacobi - module scipy.special

Signature de la fonction sh_jacobi

def sh_jacobi(n, p, q, monic=False) 

Description

sh_jacobi.__doc__

Shifted Jacobi polynomial.

    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 nth Jacobi polynomial.

    Parameters
    ----------
    n : int
        Degree of the polynomial.
    p : float
        Parameter, must have :math:`p > q - 1`.
    q : float
        Parameter, must be greater than 0.
    monic : bool, optional
        If `True`, scale the leading coefficient to be 1. Default is
        `False`.

    Returns
    -------
    G : orthopoly1d
        Shifted Jacobi polynomial.

    Notes
    -----
    For fixed :math:`p, q`, the polynomials :math:`G_n^{(p, q)}` are
    orthogonal over :math:`[0, 1]` with weight function :math:`(1 -
    x)^{p - q}x^{q - 1}`.