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

DOI10.1016/j.nuclphysb.2008.08.022zbMath1192.81351arXiv0807.0567OpenAlexW1984255374WikidataQ59869343 ScholiaQ59869343MaRDI QIDQ985858

Mikhail Yu. Kalmykov, Bernd A. Kniehl

Publication date: 6 August 2010

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0567

zbMATH Keywords

generalised hypergeometric functionsGauss hypergeometric functionsmultiple polylogarithmsmultiloop calculationsLaurent expansion about rational values of parameterstwo-loop sunset

Mathematics Subject Classification ID

Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Electromagnetic interaction; quantum electrodynamics (81V10) Approximation by rational functions (41A20) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (20)

A Feynman integral and its recurrences and associators ⋮ NumExp: numerical epsilon expansion of hypergeometric functions ⋮ Two-loop integral reduction from elliptic and hyperelliptic curves ⋮ Two-loop diagrams in nonrelativistic QCD with elliptics ⋮ Derivatives of Horn hypergeometric functions with respect to their parameters ⋮ \texttt{MultiHypExp}: a \textsc{Mathematica} package for expanding multivariate hypergeometric functions in terms of multiple polylogarithms ⋮ Differential reduction of generalized hypergeometric functions from Feynman diagrams: one-variable case ⋮ Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation ⋮ GKZ hypergeometric systems of the three-loop vacuum Feynman integrals ⋮ \(\epsilon\)-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus ⋮ On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering ⋮ The elliptic dilogarithm for the sunset graph ⋮ GKZ-hypergeometric systems for Feynman integrals ⋮ All orders structure and efficient computation of linearly reducible elliptic Feynman integrals ⋮ Algorithms to evaluate multiple sums for loop computations ⋮ Sunrise integrals with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms ⋮ Feynman integrals as A-hypergeometric functions ⋮ Harmonic sums and polylogarithms generated by cyclotomic polynomials ⋮ Hypergeometric Functions and Feynman Diagrams ⋮ Differential Equations and Feynman Integrals

Uses Software

• lsjk

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical evaluation of multiple polylogarithms
• Hypexp 2, expanding hypergeometric functions about half-integer parameters
• Hypergeometric representation of the two-loop equal mass sunrise diagram
• Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor-planar case
• Massive Feynman diagrams and inverse binomial sums
• About higher order \(\varepsilon\)-expansion of some massive two- and three-loop master-integrals
• Two-loop sunset diagrams with three massive lines
• Quantum field theory techniques in graphical enumeration
• A new hypergeometric representation of one-loop scalar integrals in \(d\) dimensions
• A generalization of Kummer's identity.
• Constructions of the Weil representations of certain simple Lie algebras
• \(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections
• Contiguous relations of hypergeometric series
• Products of two restricted hypergeometric functions
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Gröbner basis and the problem of contiguous relations
• FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS
• The Algebra of Linear Partial Difference Operators and Its Applications
• Connection between Feynman integrals having different values of the space-time dimension
• HARMONIC POLYLOGARITHMS
• Special values of multiple polylogarithms
• DUALITY FORMULAS OF THE SPECIAL VALUES OF MULTIPLE POLYLOGARITHMS
• Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
• Expansion around half-integer values, binomial sums, and inverse binomial sums
• Algebras of Iterated Path Integrals and Fundamental Groups
• New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams

This page was built for publication: Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters