HYPERDIRE—HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella functionFCof three variables

2016/02/29 by V. V. Bytev, V. Bytev, Bernd A. Kniehl +1 · 23 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebra over a field #Applied mathematics #Biology #Computer science #Differential (mechanical device) #Function (biology) #Geometry #Hypergeometric distribution #Hypergeometric function #Mathematics #Numerical methods for differential equations #Physics #Polynomial and algebraic computation #Pure mathematics #Reduction (mathematics) #cs.SC #hep-ph #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.cpc.2016.04.016

published in Computer Physics Communications 206, 78-83 (Elsevier BV) · 15 pages, minor changes, accepted for publication in Computer Physics Communications

openalex publication_date 2016/05/09 · arxiv created 2016/05/22 · openalex created_date 2016/06/24 · arxiv updated 2016/06/29 · openalex updated_date 2026/08/05

Abstract

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations. Specifically, we present the implementation of the differential reduction for the Lauricella function F_C of three variables.

Citations

• Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation
• Regularization and renormalization of gauge fields
• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• Dimensional renorinalization : The number of dimensions as a regularizing parameter
• The one-loop pentagon to higher orders in epsilon