2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 5970
author:  Christian Costermans, JeanYves 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
{(1z)
, near the singularity
α
log
β
(1z)}
α∈ℤ, β∈ℕ
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 JeanYves 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. 5970 
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