NumExp: numerical epsilon expansion of hypergeometric functions (Q310311)

scientific article; zbMATH DE number 6625262

Language	Label	Description	Also known as
English	NumExp: numerical epsilon expansion of hypergeometric functions	scientific article; zbMATH DE number 6625262

Statements

instance of

scholarly article

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title

NumExp: numerical epsilon expansion of hypergeometric functions (English)

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Computer Physics Communications

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publication date

8 September 2016

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full work available at URL

https://arxiv.org/abs/1209.3971

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zbMATH Keywords

hypergeometric functions

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expansion

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Feynman diagrams

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describes a project that uses

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Some exact results for <i>N</i>-point massive Feynman integrals

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New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams

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Connection between Feynman integrals having different values of the space-time dimension

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Application of the negative-dimension approach to massless scalar box integrals

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The two-loop scalar and tensor pentabox graph with light-like legs.

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Differential equations for two-loop four-point functions.

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A new hypergeometric representation of one-loop scalar integrals in \(d\) dimensions

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The one-loop pentagon to higher orders in \(\varepsilon \)

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Non-planar massless two-loop Feynman diagrams with four on-shell legs

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Negative-dimensional integration revisited

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Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation

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New method of massive \(N\)-point Feynman diagrams calculation

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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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Analytic result for the one-loop scalar pentagon integral with massless propagators

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Single-scale diagrams and multiple binomial sums

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\(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections

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Massive Feynman diagrams and inverse binomial sums

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

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

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

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

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HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS

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HARMONIC POLYLOGARITHMS

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Numerical evaluation of harmonic polylogarithms

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Numerical evaluation of two-dimensional harmonic polylogarithms

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Numerical evaluation of multiple polylogarithms

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HPL, a Mathematica implementation of the harmonic polylogarithms

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On the generalized harmonic polylogarithms of one complex variable

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CHAPLIN -- complex harmonic polylogarithms in Fortran

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Generation of Finite Difference Formulas on Arbitrarily Spaced Grids

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A massive Feynman integral and some reduction relations for Appell functions

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Finding new relationships between hypergeometric functions by evaluating Feynman integrals

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SecDec: A general program for sector decomposition

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Infrared behavior of three-point functions in Landau gauge Yang-Mills theory

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Numerical evaluation of Appell's \(F_1\) hypergeometric function

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F1: a code to compute Appell's \(F_{1}\) hypergeometric function

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An Analytic Continuation of the Hypergeometric Series

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Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions

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Generalized Hypergeometric Functions at Unit Argument

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Q4496211

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Partial sums of hypergeometric series of unit argument

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Q5695693

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Fast evaluation of the hypergeometric function \(_pF_{p-1}\)(a;b;z) at the singular point \(z = 1\) by means of the Hurwitz zeta function \(\xi(\alpha,s)\).

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Acceleration of generalized hypergeometric functions through precise remainder asymptotics

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Identifiers

zbMATH Open document ID

1344.33001

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Mathematics Subject Classification ID

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10.1016/J.CPC.2013.03.016

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Sitelinks

Mathematics(1 entry)

mardi Publication:310311