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

By Tobias Huber, Daniel Maître. Computer Physics Communications, 2005

308 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6d6c08165ae8740ae12d0d4e8ab62df656c1bd55

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Citations in the corpus

Soft triple-real radiation for Higgs production at N3LO (2013, methodology): “Whenever we are able to do so, we evaluate the remaining MB integrals to all orders in ǫ in terms of hypergeometric functions that can easily be expanded into a Laurent series ǫ using the HypExp package [89].”
Motivic multiple zeta values and superstring amplitudes (2012, background): “s Brown for urging him to go up to weight sixteen in the α′–expansion of the open superstring amplitude. This work has crucially beneﬁted by the great deal of computer based achievements exhibited in [34,35,19] and [36,37]. In particular, St.St. wishes to thank Thomas Hahn, Tobias Huber, Daniel Maˆı”
Analytic boosted boson discrimination (2015, methodology): “Expanding in (throughout these appendices we use the HypExp package [191, 192] for expansions of hypergeometric functions) and separating in divergent and finite pieces, we find”
Feynman integrals and hyperlogarithms (2015, background): “Several programs for their expansion are available; some are based on the integral representation [102, 103] while others use summation methods [130, 131, 181, 182].”
Two-loop soft corrections and resummation of the thrust distribution in the dijet region (2011, methodology): “We evaluate the integrals in MATHEMATICA, partly using the package HypExp [ 82 , 83].”
Calculation of the quark and gluon form factors to three loops in QCD (2010, methodology): “The one-loop and two-loop master integrals appearing in the form factors at these loop orders are displayed in figure 1. Their expansions to finite order have been known for a long time, all-orders expressions were derived in [37], they can for example be expanded using HypExp [ 77 ].”
pySecDec: A toolbox for the numerical evaluation of multi-scale integrals (2017, methodology): “order Exact result (using HypExp [42]) pySecDec result”