Module « scipy.special »

Fonction spherical_in - module scipy.special

Signature de la fonction spherical_in

def spherical_in(n, z, derivative=False) 

Description

spherical_in.__doc__

Modified spherical Bessel function of the first kind or its derivative.

    Defined as [1]_,

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

    where :math:`I_n` is the modified 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
    -------
    in : ndarray

    Notes
    -----
    The function is computed using its definitional relation to the
    modified cylindrical Bessel function of the first kind.

    The derivative is computed using the relations [2]_,

    .. math::
        i_n' = i_{n-1} - \frac{n + 1}{z} i_n.

        i_1' = i_0


    .. versionadded:: 0.18.0

    References
    ----------
    .. [1] https://dlmf.nist.gov/10.47.E7
    .. [2] https://dlmf.nist.gov/10.51.E5