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