Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams

Details Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams

2006-02-02

arxiv.org/abs/hep-th/0602028v5

JHEP0604:056,2006

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX, 1-eps figure; v5: The code (Mathematica/FORM) is available via the www http://theor.jinr.ru/~kalmykov/hyperge

Scientific paper

10.1088/1126-6708/2006/04/056

The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or half-integer values of parameters there are only three types of algebraically independent Gauss hypergeometric functions. The epsilon-expansion of functions of one of this type (type F in our classification) demands the introduction of new functions related to generalizations of elliptic functions. For the five other types of functions the higher-order epsilon-expansion up to functions of weight 4 are constructed. The result of the expansion is expressible in terms of Nielsen polylogarithms only. The reductions and epsilon-expansion of q-loop off-shell propagator diagrams with one massive line and q massless lines and q-loop bubble with two-massive lines and q-1 massless lines are considered. The code (Mathematica/FORM) is available via the www at this URL http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html

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