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 $F_D$ of $r$ variables; and the second one, FsFunction, for manipulations with Lauricella-Saran hypergeometric functions $F_S$ 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.

v3=v2: A new section 5 is added; published version

References in corpus (10)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• On form factors in N=4 sym
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• New relationships between Feynman integrals
• Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
• HQET heavy-heavy vertex diagram with two velocities
• Epsilon expansion of Appell and Kampé de Fériet functions
• Numerical calculation of one-loop integration with hypergeometric functions

Cited by in corpus (15)

• On the reduction of generalized polylogarithms to ${\text{Li}}_n$ and ${\text{Li}}_{2,2}$ and on the evaluation thereof
• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables
• Four-point function in general kinematics through geometrical splitting and reduction
• Functional reduction of one-loop Feynman integrals with arbitrary masses
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d
• Analytic continuations and numerical evaluation of the Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$ and their Application to Feynman Integrals
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• Geometrical splitting and reduction of Feynman diagrams
• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change
• Specializations of partial differential equations for Feynman integrals
• Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d, II: Special kinematics
• Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
• Counting master integrals: Integration by parts vs. functional equations