HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters

Abstract
We present the Mathematica package HypExp which allows to expand hypergeometric functions _J F_(J - 1)around integer parameters to arbitrary order. At this, we apply two methods, the first one being based on an integral representation, the second one on the nested sums approach. The expansion works for both symbolic argument z and unit argument. We also implemented new classes of integrals that appear in the first method and that are, in part, yet unknown to Mathematica.

Title of program: HypExp
Catalogue Id: ADXF_v1_0

Nature of problem
Expansion of hypergeometric functions around integer-valued parameters. These are needed in the context of dimensional regularisation for loop and phase space integrals.

Versions of this program held in the CPC repository in Mendeley Data
ADXF_v1_0; HypExp; 10.1016/j.cpc.2006.01.007
ADXF_v2_0; HypExp 2; 10.1016/j.cpc.2007.12.008
ADXF_v2_1; HypExp 2; 10.1016/j.cpc.2011.11.016

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

摘要
本文介绍Mathematica软件包HypExp，该工具可将超几何函数（hypergeometric functions）_JF_{J-1}围绕整数参数展开至任意阶数。本工具采用两种实现方法：第一种基于积分表示法，第二种基于嵌套求和方法。该展开方法同时支持符号宗量z与单位宗量的输入场景。此外，我们还实现了第一种方法中出现的新型积分类，其中部分积分此前在Mathematica中尚未被收录。

程序题名：HypExp
目录编号：ADXF_v1_0

问题属性
针对整数取值参数的超几何函数展开问题。该类展开在圈积分与相空间积分的维数正规化（dimensional regularisation）场景中具有明确的应用需求。

本程序在Mendeley数据集中的CPC程序库内的版本如下：
ADXF_v1_0; HypExp; 10.1016/j.cpc.2006.01.007
ADXF_v2_0; HypExp 2; 10.1016/j.cpc.2007.12.008
ADXF_v2_1; HypExp 2; 10.1016/j.cpc.2011.11.016

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019）