English

Harmonic sums and polylogarithms at non-positive multi-indices

Combinatorics 2016-11-30 v1 Number Theory

Abstract

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

Keywords

Cite

@article{arxiv.1611.09683,
  title  = {Harmonic sums and polylogarithms at non-positive multi-indices},
  author = {Gérard Duchamp and Hoang Ngoc and Ngo Quoc},
  journal= {arXiv preprint arXiv:1611.09683},
  year   = {2016}
}

Comments

Journal of Symbolic Computation, Elsevier, 2016

R2 v1 2026-06-22T17:08:04.007Z