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Module « scipy.special »

Fonction wright_bessel - module scipy.special

Signature de la fonction wright_bessel

def wright_bessel(*args, **kwargs) 

Description

help(scipy.special.wright_bessel)

wright_bessel(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    wright_bessel(a, b, x, out=None)

    Wright's generalized Bessel function.

    Wright's generalized Bessel function is an entire function and defined as

    .. math:: \Phi(a, b; x) = \sum_{k=0}^\infty \frac{x^k}{k! \Gamma(a k + b)}

    See Also [1].

    Parameters
    ----------
    a : array_like of float
        a >= 0
    b : array_like of float
        b >= 0
    x : array_like of float
        x >= 0
    out : ndarray, optional
        Optional output array for the function results

    Returns
    -------
    scalar or ndarray
        Value of the Wright's generalized Bessel function

    Notes
    -----
    Due to the complexity of the function with its three parameters, only
    non-negative arguments are implemented.

    .. versionadded:: 1.7.0

    References
    ----------
    .. [1] Digital Library of Mathematical Functions, 10.46.
           https://dlmf.nist.gov/10.46.E1

    Examples
    --------
    >>> from scipy.special import wright_bessel
    >>> a, b, x = 1.5, 1.1, 2.5
    >>> wright_bessel(a, b-1, x)
    4.5314465939443025

    Now, let us verify the relation

    .. math:: \Phi(a, b-1; x) = a x \Phi(a, b+a; x) + (b-1) \Phi(a, b; x)

    >>> a * x * wright_bessel(a, b+a, x) + (b-1) * wright_bessel(a, b, x)
    4.5314465939443025
    

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