Module « scipy.special »

Fonction jacobi - module scipy.special

Signature de la fonction jacobi

def jacobi(n, alpha, beta, monic=False) 

Description

jacobi.__doc__

Jacobi polynomial.

    Defined to be the solution of

    .. math::
        (1 - x^2)\frac{d^2}{dx^2}P_n^{(\alpha, \beta)}
          + (\beta - \alpha - (\alpha + \beta + 2)x)
            \frac{d}{dx}P_n^{(\alpha, \beta)}
          + n(n + \alpha + \beta + 1)P_n^{(\alpha, \beta)} = 0

    for :math:`\alpha, \beta > -1`; :math:`P_n^{(\alpha, \beta)}` is a
    polynomial of degree :math:`n`.

    Parameters
    ----------
    n : int
        Degree of the polynomial.
    alpha : float
        Parameter, must be greater than -1.
    beta : float
        Parameter, must be greater than -1.
    monic : bool, optional
        If `True`, scale the leading coefficient to be 1. Default is
        `False`.

    Returns
    -------
    P : orthopoly1d
        Jacobi polynomial.

    Notes
    -----
    For fixed :math:`\alpha, \beta`, the polynomials
    :math:`P_n^{(\alpha, \beta)}` are orthogonal over :math:`[-1, 1]`
    with weight function :math:`(1 - x)^\alpha(1 + x)^\beta`.