scipy.special.wright_bessel#
- scipy.special.wright_bessel(a, b, x) = <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
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