DMTCS

2005 International Conference on Analysis of Algorithms

Conrado Martínez (ed.)

DMTCS Conference Volume AD (2005), pp. 59-70


author: Christian Costermans, Jean-Yves Enjalbert and Hoang Ngoc Minh
title: Algorithmic and combinatoric aspects of multiple harmonic sums
keywords: polylogarithms, polyzêtas, multiple harmonic sums, singular expansion, shuffle algebra, Lyndon words
abstract: Ordinary generating series of multiple harmonic sums admit a full singular expansion in the basis of functions
{(1-z)
α
log
β
(1-z)}
α∈ℤ, β∈ℕ
, near the singularity
z=1
. A constructive proof of this result is given, and, by combinatoric aspects, an explicit evaluation of Taylor coefficients of functions in some polylogarithmic algebra is obtained. In particular, the asymptotic expansion of multiple harmonic sums is easily deduced.
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reference: Christian Costermans and Jean-Yves Enjalbert and Hoang Ngoc Minh (2005), Algorithmic and combinatoric aspects of multiple harmonic sums, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 59-70
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