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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2005

Algorithmic and combinatoric aspects of multiple harmonic sums

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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Dates and versions

hal-01184041 , version 1 (12-08-2015)

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Christian Costermans, Jean-Yves Enjalbert, Hoang Ngoc Minh. Algorithmic and combinatoric aspects of multiple harmonic sums. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.59-70, ⟨10.46298/dmtcs.3369⟩. ⟨hal-01184041⟩

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