Module « scipy.special »

Fonction lpmn - module scipy.special

Signature de la fonction lpmn

def lpmn(m, n, z) 

Description

lpmn.__doc__

Sequence of associated Legendre functions of the first kind.

    Computes the associated Legendre function of the first kind of order m and
    degree n, ``Pmn(z)`` = :math:`P_n^m(z)`, and its derivative, ``Pmn'(z)``.
    Returns two arrays of size ``(m+1, n+1)`` containing ``Pmn(z)`` and
    ``Pmn'(z)`` for all orders from ``0..m`` and degrees from ``0..n``.

    This function takes a real argument ``z``. For complex arguments ``z``
    use clpmn instead.

    Parameters
    ----------
    m : int
       ``|m| <= n``; the order of the Legendre function.
    n : int
       where ``n >= 0``; the degree of the Legendre function.  Often
       called ``l`` (lower case L) in descriptions of the associated
       Legendre function
    z : float
        Input value.

    Returns
    -------
    Pmn_z : (m+1, n+1) array
       Values for all orders 0..m and degrees 0..n
    Pmn_d_z : (m+1, n+1) array
       Derivatives for all orders 0..m and degrees 0..n

    See Also
    --------
    clpmn: associated Legendre functions of the first kind for complex z

    Notes
    -----
    In the interval (-1, 1), Ferrer's function of the first kind is
    returned. The phase convention used for the intervals (1, inf)
    and (-inf, -1) is such that the result is always real.

    References
    ----------
    .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
           Functions", John Wiley and Sons, 1996.
           https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html
    .. [2] NIST Digital Library of Mathematical Functions
           https://dlmf.nist.gov/14.3