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.
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