Evaluating Generating Functions for Periodic Multiple Polylogarithms via Rational Chen–Fliess Series
| Autor: | Kurusch Ebrahimi-Fard, Dominique Manchon, W. Steven Gray |
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| Rok vydání: | 2020 |
| Předmět: |
Polylogarithm
Conjecture Series (mathematics) biology Generating function Bilinear interpolation biology.organism_classification Dynamical system Algebra Chen TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Realization (systems) Mathematics |
| Zdroj: | Springer Proceedings in Mathematics & Statistics ISBN: 9783030370305 |
| DOI: | 10.1007/978-3-030-37031-2_17 |
| Popis: | The goal of the paper is to give a systematic way to numerically evaluate the generating function of a periodic multiple polylogarithm using a Chen–Fliess series with a rational generating series. The idea is to realize the corresponding Chen–Fliess series as a bilinear dynamical system. A standard form for such a realization is given. The method is also generalized to the case where the multiple polylogarithm has non-periodic components. This allows one, for instance, to numerically validate the Hoffman conjecture. Finally, a setting in terms of dendriform algebras is provided. |
| Databáze: | OpenAIRE |
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