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

2004/02/12 by Stefan Weinzierl · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Algebra over a field #Applied mathematics #Binomial (polynomial) #Binomial coefficient #Binomial theorem #Central binomial coefficient #Combinatorics #Computer science #Discrete mathematics #Extension (predicate logic) #Gaussian binomial coefficient #Integer (computer science) #Inverse #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Negative binomial distribution #Poisson distribution #Polynomial and algebraic computation #Pure mathematics #Statistics #Transcendental function #Transcendental number #hep-ph #hep-th

paper · pdf · doi:10.1063/1.1758319

published as J.Math.Phys. 45 (2004) 2656-2673 · 21 pages

arxiv created 2004/02/12 · openalex publication_date 2004/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof.

Citations

• Special values of multiple polylogarithms
• vs. pole masses of gauge bosons II: two-loop electroweak fermion corrections
• Analytic two-loop results for self-energy- and vertex-type diagrams with one non-zero mass
• HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
• Multiple singular emission in gauge theories
• Harmonic Polylogarithms

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