Hypergeometric Functions and Feynman Diagrams

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as 2F1 Gauß hypergeomet...

Differential reduction of generalized hypergeometric functions in application to Feynman diagrams: One-variable case

The differential reduction algorithm which allow one to express generalized hypergeometric functions with arbitrary values of parameters in terms of functions with fixed values of parameters differing from the original ones by integers is discussed in a context of evaluation of Feynman diagrams. Where it is possible we make a comparison between our results and ones based on a standard technique...

Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is...

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

The Gauss hypergeometric functions 2 F 1 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 hyperge-ometric functions. The ε-expansion of functions of one of ...

Feynman diagrams versus Fermi-gas Feynman emulator