Kleene stars of the plane, polylogarithms and symmetries
Symbolic Computation
2020-02-21 v2 Discrete Mathematics
Combinatorics
Abstract
We extend the definition and construct several bases for polylogarithms Li T , where T are some series, recognizable by a finite state (multiplicity) automaton of alphabet 4 X = {x 0 , x 1 }. The kernel of this new "polylogarithmic map" Li is also characterized and provides a rewriting process which terminates to a normal form. We concentrate on algebraic and analytic aspects of this extension allowing index polylogarithms at non positive multi-indices, by rational series and regularize polyzetas at non positive multi-indices.
Keywords
Cite
@article{arxiv.1811.09091,
title = {Kleene stars of the plane, polylogarithms and symmetries},
author = {Gérard Henry Edmond Duchamp and Vincel Hoang Ngoc Minh and Ngo Quoc Hoan},
journal= {arXiv preprint arXiv:1811.09091},
year = {2020}
}