Mikhail Yu. Kalmykov

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We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iterated solutions to the differential equations associated with hypergeometric functions to prove the following result: Theorem 1: The(More)
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(More)
∗Speaker. †This work was supported in part by the German Federal Ministry for Education and Research BMBF through Grant No. 05 HT6GUA, by the German Research Foundation DFG through the Collaborative Research Centre No. 676 Particles, Strings and the Early Universe—The Structure of Matter and Space-Time, and by the Helmholtz Association HGF through the(More)
We prove the following theorems: 1) The Laurent expansions in ε of the Gauss hypergeometric functions 2F1(I1 + aε, I2 + bε; I3 + p q + cε; z), 2F1(I1 + p q + aε, I2 + p q + bε; I3+ p q + cε; z) and 2F1(I1+ p q +aε, I2+ bε; I3 + p q + cε; z), where I1, I2, I3, p, q are arbitrary integers, a, b, c are arbitrary numbers and ε is an infinitesimal parameter, are(More)
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions FD of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran(More)
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions FD of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran(More)