A numerical evaluator for the generalized hypergeometric series

Abstract
The generalized hypergeometric series is numerically evaluated using extended precision subroutines. Cases involving large, complex arguments are shown to be accurate up to 12 significant figures.

Title of program: PFQ
Catalogue Id: ACPA_v1_0

Nature of problem
The generalized hypergeometric series is the solution of many equations occuring in various scientific and engineering disciplines. A couple of examples are: the radial part of the wavefunction of the hydrogen atom, for bound and continuum states both non-relativistic and relativistic, and the radial and angular parts of the solution to the biconical antenna.

Versions of this program held in the CPC repository in Mendeley Data
ACPA_v1_0; PFQ; 10.1016/0010-4655(93)90008-Z

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本研究采用高精度子程序（extended precision subroutines）对广义超几何级数（generalized hypergeometric series）进行数值求值，结果表明，针对含大型复宗量的算例，计算精度可达12位有效数字。

程序名称：PFQ
目录编号：ACPA_v1_0

问题本质
广义超几何级数是诸多科学与工程领域中大量方程的解。典型应用案例包括：非相对论与相对论框架下氢原子束缚态及连续态波函数的径向分量，以及双锥天线（biconical antenna）求解结果的径向与角向分量。

孟德莱数据（Mendeley Data）平台CPC库中收录的该程序版本：ACPA_v1_0；PFQ；10.1016/0010-4655(93)90008-Z

本程序源自贝尔法斯特女王大学（1969-2019年）维护的CPC程序库。