scipy.special.wright_bessel

scipy.special.wright_bessel(a, b, x, out=None) = <ufunc 'wright_bessel'>

Wright’s generalized Bessel function.

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

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

See also [1].

Parameters:

aarray_like of float

a >= 0

barray_like of float

b >= 0

xarray_like of float

x >= 0

outndarray, optional

Optional output array for the function results

Returns:

scalar or ndarray

Value of the Wright’s generalized Bessel function

Notes

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

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

\[\Phi(a, b-1; x) = a x \Phi(a, b+a; x) + (b-1) \Phi(a, b; x)\]

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