Module « scipy.special »

Fonction wright_bessel - module scipy.special

Signature de la fonction wright_bessel

Description

wright_bessel.__doc__

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

wright_bessel(a, b, x)

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

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

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

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