HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: $F_D$ and $F_S$ Horn-type hypergeometric functions of three variables
Abstract
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 of variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions of three variables. Both functions are related with one-loop Feynman diagrams. The published version includes also Chapter 5 with two theorems about structure of coefficients of epsilon-expansion of the Horn-type hypergeometric functions. As illustration, the first three coefficients of epsilon-expansion for the Appell hypergeometric function FD of r-variables are explicitly evaluated.
Keywords
Cite
@article{arxiv.1312.5777,
title = {HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: $F_D$ and $F_S$ Horn-type hypergeometric functions of three variables},
author = {Vladimir V. Bytev and Mikhail Yu. Kalmykov and Sven-Olaf Moch},
journal= {arXiv preprint arXiv:1312.5777},
year = {2014}
}
Comments
v3=v2: A new section 5 is added; published version