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 F J − 1 J 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. Program summary Title of program:HypExp Catalogue identifier:ADXF_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXF_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licence:none Computers:Computers running Mathematica under Linux or Windows Operating system: Linux, Windows Program language: Mathematica No. of bytes in distributed program, including test data, etc.:739 410 No. of lines in distributed program, including test data, etc.:89 747 Distribution format:tar.gz Other package needed:the package HPL, included in the distribution External file required:none Nature of the physical problem:Expansion of hypergeometric functions around integer-valued parameters. These are needed in the context of dimensional regularization for loop and phase space integrals. Method of solution:Algebraic manipulation of nested sums and integral representation. Restrictions on complexity of the problem:Limited by the memory available Typical running time:Strongly depending on the problem and the availability of libraries.