Module « scipy.special »

Fonction spherical_jn - module scipy.special

Signature de la fonction spherical_jn

def spherical_jn(n, z, derivative=False) 

Description

spherical_jn.__doc__

Spherical Bessel function of the first kind or its derivative.

    Defined as [1]_,

    .. math:: j_n(z) = \sqrt{\frac{\pi}{2z}} J_{n + 1/2}(z),

    where :math:`J_n` is the Bessel function of the first kind.

    Parameters
    ----------
    n : int, array_like
        Order of the Bessel function (n >= 0).
    z : complex or float, array_like
        Argument of the Bessel function.
    derivative : bool, optional
        If True, the value of the derivative (rather than the function
        itself) is returned.

    Returns
    -------
    jn : ndarray

    Notes
    -----
    For real arguments greater than the order, the function is computed
    using the ascending recurrence [2]_. For small real or complex
    arguments, the definitional relation to the cylindrical Bessel function
    of the first kind is used.

    The derivative is computed using the relations [3]_,

    .. math::
        j_n'(z) = j_{n-1}(z) - \frac{n + 1}{z} j_n(z).

        j_0'(z) = -j_1(z)


    .. versionadded:: 0.18.0

    References
    ----------
    .. [1] https://dlmf.nist.gov/10.47.E3
    .. [2] https://dlmf.nist.gov/10.51.E1
    .. [3] https://dlmf.nist.gov/10.51.E2