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- M. Yu. Kalmykov
- 2007

We continue the study of the construction of analytical coefficients of the ε-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums

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)

- Vladimir V. Bytev, Mikhail Yu. Kalmykov, Bernd A. Kniehl
- ArXiv
- 2009

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)

- Vladimir V. Bytev, Mikhail Yu. Kalmykov, Sven-Olaf Moch
- ArXiv
- 2013

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)

- Vladimir V. Bytev, Mikhail Yu. Kalmykov, Sven-Olaf Moch, LONG WRITE-UP
- 2013

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)

- Vladimir V. Bytev, Mikhail Yu. Kalmykov, Sven-Olaf Moch
- Computer Physics Communications
- 2014

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)

- M. Yu. Kalmykov
- 1998

The renormalization group method in R2-gravity without matter fields is discussed. A criterion for the existence of the renormalization constant for the metric has been found, two-loop higher order poles have been calculated, a relation which allows us to find the one-loop renormalization constant of the Newtonian constant has been suggested. PACS numbers:… (More)

- Vladimir V. Bytev, Mikhail Yu. Kalmykov, Bernd A. Kniehl
- ArXiv
- 2011