Christian Costermans ; Jean-Yves Enjalbert ; Hoang Ngoc Minh - Algorithmic and combinatoric aspects of multiple harmonic sums

dmtcs:3369 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3369
Algorithmic and combinatoric aspects of multiple harmonic sumsArticle

Authors: Christian Costermans 1; Jean-Yves Enjalbert 1; Hoang Ngoc Minh 1

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.


Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: singular expansion,multiple harmonic sums,Lyndon words,shuffle algebra,polylogarithms,polyzêtas,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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