Module « scipy.special »

Fonction chebyu - module scipy.special

Signature de la fonction chebyu

def chebyu(n, monic=False) 

Description

chebyu.__doc__

Chebyshev polynomial of the second kind.

    Defined to be the solution of

    .. math::
        (1 - x^2)\frac{d^2}{dx^2}U_n - 3x\frac{d}{dx}U_n
          + n(n + 2)U_n = 0;

    :math:`U_n` is a polynomial of degree :math:`n`.

    Parameters
    ----------
    n : int
        Degree of the polynomial.
    monic : bool, optional
        If `True`, scale the leading coefficient to be 1. Default is
        `False`.

    Returns
    -------
    U : orthopoly1d
        Chebyshev polynomial of the second kind.

    Notes
    -----
    The polynomials :math:`U_n` are orthogonal over :math:`[-1, 1]`
    with weight function :math:`(1 - x^2)^{1/2}`.

    See Also
    --------
    chebyt : Chebyshev polynomial of the first kind.