HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
arXiv:0708.2443 · doi:10.1016/j.cpc.2007.12.008
Abstract
In this article, we describe a new algorithm for the expansion of hypergeometric functions about half-integer parameters. The implementation of this algorithm for certain classes of hypergeometric functions in the already existing Mathematica package HypExp is described. Examples of applications in Feynman diagrams with up to four loops are given.
38 pages, 7 figures. Minor changes. Version to appear in CPC. The package can be downloaded from http://krone.physik.unizh.ch/~maitreda/HypExp/
References in corpus (41)
- Harmonic Polylogarithms
- Differential Equations for Two-Loop Four-Point Functions
- HPL, a Mathematica implementation of the harmonic polylogarithms
- HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
- Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
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- Four-Particle Phase Space Integrals in Massless QCD
- Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity
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- Standard and epsilon-finite Master Integrals for the rho-Parameter
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