English

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

Mathematical Physics 2014-10-27 v3 Symbolic Computation High Energy Physics - Phenomenology High Energy Physics - Theory math.MP

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 FDF_D of rr variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions FSF_S 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