HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two 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 allows for manipulations involving the full set of Horn-type hypergeometric functions of two variables, including 30 functions.

minor corrections, publushed version

References in corpus (10)

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• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• Counting master integrals: integration by parts vs. differential reduction
• Series and epsilon-expansion of the hypergeometric functions
• 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
• Hypergeometric functions, their epsilon expansions and Feynman diagrams
• Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions
• When epsilon-expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variables examples

Cited by in corpus (36)

• Feynman integrals as A-hypergeometric functions
• Evaluation of the general 3-loop vacuum Feynman integral
• Effective potential at three loops
• 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
• GKZ-hypergeometric systems for Feynman integrals
• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• From positive geometries to a coaction on hypergeometric functions
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• Counting master integrals: integration by parts vs. differential reduction
• Three-loop vacuum integrals with arbitrary masses
• HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables
• Evaluating Feynman integrals by the hypergeometry
• The system of partial differential equations for the $C_{{}_0}$ function
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d
• TVID: Three-loop Vacuum Integrals from Dispersion relations
• The propagator seagull: general evaluation of a two loop diagram
• The vacuum seagull: evaluating a 3-loop Feynman diagram with 3 mass scales
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• The real-virtual antenna functions for $S\to Q\bar{Q}X$ at NNLO QCD
• When epsilon-expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variables examples
• 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
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Analytic calculation of doubly heavy hadron spectral density in coordinate space
• Specializations of partial differential equations for Feynman integrals
• The four-propagator three-loop vacuum integral by the hypergeometry
• Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d, II: Special kinematics
• Two-loop Feynman integrals for ${\varphi }^4$ theory with long-range correlated disorder
• Evaluation of three-loop self-energy master integrals with four or five propagators
• Counting master integrals: Integration by parts vs. functional equations
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals