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- M. Yu. Kalmykov
- 2007

Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter Abstract: 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,… (More)

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 hy-pergeometric 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)

- 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 F D of r variables; and the second one, FsFunction, for manipulations with Lauricella-Saran… (More)

We prove the following theorems: 1) The Laurent expansions in ε of the Gauss hypergeometric functions 2

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… (More)

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

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

- Vladimir V. Bytev, Mikhail Yu. Kalmykov, Bernd A. Kniehl
- Computer Physics Communications
- 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: one, pfq, is relevant for manipulations of hypergeometric functions_{p+1}F_p, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions… (More)

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