Hypergeometric functions, their epsilon expansions and Feynman diagrams
arXiv:0810.3238
Abstract
We review the hypergeometric function approach to Feynman diagrams. Special consideration is given to the construction of the Laurent expansion. As an illustration, we describe a collection of physically important one-loop vertex diagrams for which this approach is useful.
15 pages, Latex, 1-eps figure; v2: few references added; v3: style corrections; v4: typo in Eq.(2) is corrected; based on a talk given by M.Kalmykov at 15th International Seminar on High-Energy Physics: Quarks-2008,Sergiev Posad, Russia, 23-29 May, 2008. The FORM code is available via the WWW at http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html
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Cited by in corpus (8)
- Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
- HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
- HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
- Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
- Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation
- The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
- Analytic Periods via Twisted Symmetric Squares
- Chinese Magic in Loop Integrals