\texttt{MultiHypExp}: a \textsc{Mathematica} package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms

DOI10.1016/j.cpc.2023.109060arXiv2306.11718OpenAlexW4389990750MaRDI QIDQ6124636

Souvik Bera

Publication date: 28 March 2024

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.11718

zbMATH Keywords

series expansionPfaffian systemFeynman integralsmultiple polylogarithmsmultivariate hypergeometric functions

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gamma, beta and polygamma functions (33B15) Feynman diagrams (81T18) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05) Higher logarithm functions (33B30) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

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• Magnus and Dyson series for master integrals
• Pfaffian of Appell's hypergeometric system \(\mathcal{F}_4\) in terms of the intersection form of twisted cohomology groups
• NumExp: numerical epsilon expansion of hypergeometric functions
• HYPERDIRE HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Horn-type hypergeometric functions of two variables
• Hypergeometric functions differential reduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: \(F_D\) and \(F_S\) Horn-type hypergeometric functions of three variables
• A new approach to the epsilon expansion of generalized hypergeometric functions
• A symbolic summation approach to Feynman integral calculus
• On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters
• CHAPLIN -- complex harmonic polylogarithms in Fortran
• A fast approach to creative telescoping
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Numerical evaluation of multiple polylogarithms
• XSummer -- transcendental functions and symbolic summation in form
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Hypexp 2, expanding hypergeometric functions about half-integer parameters
• Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems
• Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation
• Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters
• Generalized Euler integrals and \(A\)-hypergeometric functions
• Extending the factorization principle to hypergeometric series of general form
• Symbolic expansion of transcendental functions
• HYPERDIRE -- hypergeometric functions differential reduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function \(F_C\) of three variables
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• \texttt{epsilon}: a tool to find a canonical basis of master integrals
• Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\)
• Functional reduction of one-loop Feynman integrals with arbitrary masses
• Mellin-Barnes integrals. A primer to particle physics applications
• Feynman integrals as A-hypergeometric functions
• Rationalizing roots: an algorithmic approach
• Reducing differential equations for multiloop master integrals
• Numerical implementation of harmonic polylogarithms to weight w = 8
• MONODROMY AND PFAFFIAN OF LAURICELLA^|^apos;S FD IN TERMS OF THE INTERSECTION FORMS OF TWISTED (CO)HOMOLOGY GROUPS
• Gröbner basis and the problem of contiguous relations
• Theory of Hypergeometric Functions
• Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
• Expansion around half-integer values, binomial sums, and inverse binomial sums
• On some formulas for the Horn functions H₁(a,b,c;d;w,z) and H₁^(c)(a,b;d;w,z)
• Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions
• Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms
• Numerical evaluation of harmonic polylogarithms
• Hypergeometric structures in Feynman integrals