Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter

Abstract

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth (see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions. Theorem B: The epsilon expansion of a hypergeometric function with one half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are ratios of polynomials. Some extra materials are available via the www at this http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html

24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected and a few references added; v3: few references added;

References in corpus (10)

• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
• Hypergeometric representation of the two-loop equal mass sunrise diagram
• A class of series acceleration formulae for Catalan's constant
• The two-loop vector form factor in the Sudakov limit
• Series and epsilon-expansion of the hypergeometric functions
• Hypergeometric representation of a four-loop vacuum bubble
• On one master integral for three-loop on-shell HQET propagator diagrams with mass
• Planar two-loop master integrals for massive Bhabha scattering: N_f=1 and N_f=2

Cited by in corpus (24)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Collider Physics at the Precision Frontier
• Iterated Binomial Sums and their Associated Iterated Integrals
• From multiple unitarity cuts to the coproduct of Feynman integrals
• Feynman integrals as A-hypergeometric functions
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• Angular integrals in d dimensions
• Higgs boson contribution to the leading two-loop Yukawa corrections to $gg\to HH$
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: $F_D$ and $F_S$ Horn-type hypergeometric functions of three variables
• On the all-order epsilon-expansion of generalized hypergeometric functions with integer values of parameters
• NumExp: Numerical epsilon expansion of hypergeometric functions
• Disordered O(n) Loop Model and Coupled Conformal Field Theories
• Apéry-Type Series and Colored Multiple Zeta Values
• Multiple zeta values, WZ-pairs and infinite sums computations
• Hypergeometric functions with rational arguments
• Chinese Magic in Loop Integrals
• Explicit Evaluation of Euler-Apéry Type Multiple Zeta Star Values and Multiple $t$-Star Values