On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters
From MaRDI portal
Publication:445770
DOI10.1088/1126-6708/2007/11/009zbMath1245.33007arXiv0708.0803OpenAlexW3105657791MaRDI QIDQ445770
Scott A. Yost, Bennie F. L. Ward, Mikhail Yu. Kalmykov
Publication date: 26 August 2012
Published in: Journal of High Energy Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0708.0803
Generalized hypergeometric series, ({}_pF_q) (33C20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Higher logarithm functions (33B30)
Related Items (16)
A Feynman integral and its recurrences and associators ⋮ NumExp: numerical epsilon expansion of hypergeometric functions ⋮ On the reduction of generalized polylogarithms to \(\mathrm{Li}_n\) and \(\mathrm{Li}_{2,2}\) and on the evaluation thereof ⋮ Hypergeometric structures in Feynman integrals ⋮ \texttt{MultiHypExp}: a \textsc{Mathematica} package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms ⋮ \(\epsilon\)-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus ⋮ The local Gromov-Witten theory of \({\mathbb{C}\mathbb{P}^1}\) and integrable hierarchies ⋮ On the field theory expansion of superstring five point amplitudes ⋮ Acceleration of generalized hypergeometric functions through precise remainder asymptotics ⋮ Derivatives of any Horn-type hypergeometric functions with respect to their parameters ⋮ Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms ⋮ Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions ⋮ Massless on-shell box integral with arbitrary powers of propagators ⋮ Two-loop Feynman integrals for ϕ4 theory with long-range correlated disorder ⋮ Hypergeometric Functions and Feynman Diagrams ⋮ Differential equations, associators, and recurrences for amplitudes
Cites Work
- XSummer -- transcendental functions and symbolic summation in form
- Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
- Massive Feynman diagrams and inverse binomial sums
- Symbolic expansion of transcendental functions
- \(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections
- Contiguous relations of hypergeometric series
- FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS
- Nielsen’s Generalized Polylogarithms
- Singular perturbation approach to traveling wave solutions of the Hodgkin-Huxley equations and its application to stability problems
- Connection between Feynman integrals having different values of the space-time dimension
- HARMONIC POLYLOGARITHMS
- Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
- Expansion around half-integer values, binomial sums, and inverse binomial sums
- On Nielsen's generalized polylogarithms and their numerical calculation
- Algebras of Iterated Path Integrals and Fundamental Groups
- The contiguous function relations for _{𝑝}𝐹_{𝑞} with application to Batemean’s 𝐽_{𝑛}^{𝑢,𝜈} and Rice’s 𝐻_{𝑛}(𝜁,𝑝,𝜈)
- Single-scale diagrams and multiple binomial sums
- Non-planar massless two-loop Feynman diagrams with four on-shell legs
- New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams
This page was built for publication: On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters
