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 complexity of the function with its three parameters, only non-negative arguments are implemented. - Added in version 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 \[\Phi(a, b-1; x) = a x \Phi(a, b+a; x) + (b-1) \Phi(a, b; x)\]- >>> a * x * wright_bessel(a, b+a, x) + (b-1) * wright_bessel(a, b, x) 4.5314465939443025