scipy.special.pbwa

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

Parabolic cylinder function W.

The function is a particular solution to the differential equation

\[y'' + \left(\frac{1}{4}x^2 - a\right)y = 0,\]

for a full definition see section 12.14 in [1].

Parameters

aarray_like

Real parameter

xarray_like

Real argument

outndarray, optional

Optional output array for the function results

Returns

wscalar or ndarray

Value of the function

wpscalar or ndarray

Value of the derivative in x

Notes

The function is a wrapper for a Fortran routine by Zhang and Jin [2]. The implementation is accurate only for |a|, |x| < 5 and returns NaN outside that range.

References

1

Digital Library of Mathematical Functions, 14.30. https://dlmf.nist.gov/14.30

2

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html