Expansion of hypergeometric functions in terms of polylogarithms with a nontrivial change of variables (Q6600265)

scientific article; zbMATH DE number 7908849

Language	Label	Description	Also known as
English	Expansion of hypergeometric functions in terms of polylogarithms with a nontrivial change of variables	scientific article; zbMATH DE number 7908849

Statements

instance of

scholarly article

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title

Expansion of hypergeometric functions in terms of polylogarithms with a nontrivial change of variables (English)

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author

M. A. Bezuglov

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Andrei I. Onishchenko

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published in

Theoretical and Mathematical Physics

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publication date

9 September 2024

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zbMATH Keywords

generalized hypergeometric functions

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Appell and Lauricella functions

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Mellin-Barnes integrals. A primer to particle physics applications

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Q5393662

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MB tools reloaded

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{\sf MBsums} --- a {\sf Mathematica} Package for the Representation of Mellin--Barnes Integrals by Multiple Sums

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On the resolution of singularities of multiple Mellin-Barnes integrals

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AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

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Automatized analytic continuation of Mellin-Barnes integrals

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Hypergeometric representation of the two-loop equal mass sunrise diagram

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Space-time dimensionality \(\mathcal D\) as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to \(\mathcal D\)

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Functional reduction of one-loop Feynman integrals with arbitrary masses

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Non-planar elliptic vertex

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Hypergeometric structures in Feynman integrals

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General hypergeometric systems of equations and series of hypergeometric type

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Q4293510

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Generalized Euler integrals and \(A\)-hypergeometric functions

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Feynman integrals as A-hypergeometric functions

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Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems

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\texttt{FeynGKZ}: a \textit{Mathematica} package for solving Feynman integrals using GKZ hypergeometric systems

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Massive Feynman diagrams and inverse binomial sums

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On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters

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Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters

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A new approach to the epsilon expansion of generalized hypergeometric functions

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Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions

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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals

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Expansion around half-integer values, binomial sums, and inverse binomial sums

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Hypergeometric Functions and Feynman Diagrams

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\(\epsilon\)-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus

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Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters

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Hypexp 2, expanding hypergeometric functions about half-integer parameters

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XSummer -- transcendental functions and symbolic summation in form

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Symbolic expansion of transcendental functions

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Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

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NumExp: numerical epsilon expansion of hypergeometric functions

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Multiple polylogarithms, cyclotomy and modular complexes

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Galois symmetries of fundamental groupoids and noncommutative geometry

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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes

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Mathematical Aspects of Scattering Amplitudes

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From polygons and symbols to polylogarithmic functions

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Numerical evaluation of multiple polylogarithms

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Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals

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MPL -- a program for computations with iterated integrals on moduli spaces of curves of genus zero

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\texttt{handyG} -- rapid numerical evaluation of generalised polylogarithms in Fortran

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Differential equations for two-loop four-point functions.

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FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS

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Lectures on differential equations for Feynman integrals

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Reducing differential equations for multiloop master integrals

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\textsf{HYPERDIRE}, hypergeometric functions differential reduction: Mathematica-based packages for differential reduction of generalized hypergeometric functions \(_pF_{p - 1}\), \(F_1\), \(F_2\), \(F_3\), \(F_4\)

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HYPERDIRE HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Horn-type hypergeometric functions of two variables

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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

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HYPERDIRE -- hypergeometric functions differential reduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function \(F_C\) of three variables

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Q5820721

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Multiple Hypergeometric Series: Appell Series and Beyond

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Advanced applications of the holonomic systems approach

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Harmonic sums and polylogarithms generated by cyclotomic polynomials

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Three-loop effective potential of general scalar theory via differential equations

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\texttt{Libra}: a package for transformation of differential systems for multiloop integrals

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\texttt{epsilon}: a tool to find a canonical basis of master integrals

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Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form

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Identifiers

zbMATH Open document ID

1547.33007

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DOI

10.1134/s0040577924060011

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6600265