$\epsilon$-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus (Q2691945)

scientific article; zbMATH DE number 7669809

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English	$\epsilon$-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus	scientific article; zbMATH DE number 7669809

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scholarly article

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title

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

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author

Souvik Bera

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publication date

30 March 2023

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full work available at URL

https://arxiv.org/abs/2208.01000

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describes a project that uses

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A new hypergeometric representation of one-loop scalar integrals in $d$ dimensions

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Evaluating Feynman integrals by the hypergeometry

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The system of partial differential equations for the $C_{0}$ function

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Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension $d$

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Functional reduction of one-loop Feynman integrals with arbitrary masses

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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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GKZ-hypergeometric systems for Feynman integrals

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

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pySecDec: a toolbox for the numerical evaluation of multi-scale integrals

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FIESTA5: numerical high-performance Feynman integral evaluation

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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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XSummer -- transcendental functions and symbolic summation in form

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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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NumExp: numerical epsilon expansion of 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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Symbolic expansion of transcendental functions

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HARMONIC POLYLOGARITHMS

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HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS

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Algebraic relations between harmonic sums and associated quantities.

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Massive Feynman diagrams and inverse binomial sums

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Derivatives of any order of the confluent hypergeometric function F11(a,b,z) with respect to the parameter a or b

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Derivatives of any order of the Gaussian hypergeometric function2F1(a,b,c;z) with respect to the parametersa,bandc

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Derivatives of any order of the hypergeometric functionpFq(a1, …,ap;b1, …,bq;z) with respect to the parametersaiandbi

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Derivatives of Horn hypergeometric functions with respect to their parameters

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Derivatives of any Horn-type hypergeometric functions with respect to their parameters

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Gröbner basis and the problem of contiguous relations

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Differentiation formulas of some hypergeometric functions with respect to all parameters

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Parameter derivatives of the generalized hypergeometric function

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On convergent series representations of Mellin-Barnes integrals

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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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Q4394947

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A fast approach to creative telescoping

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Advanced applications of the holonomic systems approach

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Horn's hypergeometric functions with three variables

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Analytic continuation of the Horn hypergeometric series with an arbitrary number of variables

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Analytic continuation of the Lauricella function with arbitrary number of variables

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Analytic continuation of Lauricella's functions , and

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On the evaluation of the Appell $F_2$ double hypergeometric function

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HPL, a Mathematica implementation of the harmonic polylogarithms

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published in

Nuclear Physics B

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.NUCLPHYSB.2023.116145

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Mathematics(1 entry)

mardi Publication:2691945

\(\epsilon\)-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus (Q2691945)

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Identifiers

Sitelinks

Mathematics(1 entry)