HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables

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.

15 pages, minor changes, accepted for publication in Computer Physics Communications

References in corpus (8)

• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• 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
• Counting master integrals: integration by parts vs. differential reduction
• Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
• Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation
• "Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view
• When epsilon-expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variables examples

Cited by in corpus (11)

• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Feynman integrals as A-hypergeometric functions
• GKZ-hypergeometric systems for Feynman integrals
• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• GKZ-system of the 2-loop self energy with 4 propagators
• Feynman Integrals of Grassmannians
• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• Specializations of partial differential equations for Feynman integrals
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals