Harmonic sums and polylogarithms at non-positive multi-indices. (November 2017)

• Record Type: Journal Article
• Authors: Duchamp, G.H.E.; Hoang Ngoc Minh, V.; Ngo, Quoc Hoan
• Is Part Of: Journal of symbolic computation. Volume 83(2017)
• Page Start: 166
• Page End: 186
• Publication Date: 2017-11
• Subjects: Harmonic sums -- Polylogarithms -- Bernoulli polynomials -- Multi-Eulerian polynomials -- Bernoulli numbers -- Eulerian numbers; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.11.010
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Extending Eulerian polynomials and Faulhaber's formula, 1 we study several combinatorial aspects of harmonic sums and polylogarithms at non-positive multi-indices as well as their structure. Our techniques are based on the combinatorics of noncommutative generating series in the shuffle Hopf algebras giving a global process to renormalize the divergent polyzetas at non-positive multi-indices.