`scipy.special._orthogonal:_pbcf`

source: /scipy/special/_orthogonal.py :1064

Signature

def _pbcf ( n , theta )

Summary

Asymptotic series expansion of parabolic cylinder function

Extended Summary

The implementation is based on sections 3.2 and 3.3 from the original paper. Compared to the published version this code adds one more term to the asymptotic series. The detailed formulas can be found at [parabolic-asymptotics]. The evaluation is done in a transformed variable $θ := arccos (t)$ where $t := x / μ$ and $μ := 2 n + 1$ .

Parameters

n : int: Quadrature order
theta : ndarray: Transformed position variable

Returns

U : ndarray: Value of the parabolic cylinder function $U (a, θ)$ .
Ud : ndarray: Value of the derivative $U^{'} (a, θ)$ of the parabolic cylinder function.

Aliases