Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments

Published: 01-12-1998| Version 1 | DOI: 10.17632/bk5vrkvz3g.1
J. Segura,
A. Gil


Abstract We present two codes to evaluate Parabolic Cylinder Functions {V(a, x), U(a, x)} for integer and half-integer positive values of a and for nonnegative x. The codes are based on the forward application of the recurrence relation for V(a, x), the backward recurrence for U(a, x), the Wronskian relation between V(a, x) and U(a, x), and the evaluation of a continued fraction for the ratio U(a, x)/U(a - 1, x). The accuracy obtained is better than 10^(-12)for 0 < x < 1.0 and better than 10^(-14) ... Title of program: DINPCF, DHAPCF Catalogue Id: ADIV_v1_0 Nature of problem We include two codes in order to evaluate Parabolic Cylinder functions of integral orders (subroutine DINPCF) and half-integral orders (subroutine DHAPCF). The codes evaluate the Parabolic Cylinder functions V(a,x) and U(a,x) (a integer or half-integer) from the lowest (non negative) order to a maximum (positive) order in the same run and store such values. Half-integral order PCF's find their application in problems with parabolic cylinder geometries. Integral order PCF's appear, for instance, ... Versions of this program held in the CPC repository in Mendeley Data ADIV_v1_0; DINPCF, DHAPCF; 10.1016/S0010-4655(98)00097-6 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)