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arXiv · 1603.05948

Evaluating Generating Functions for Periodic Multiple Polylogarithms

Kurusch Ebrahimi-Fard·W. Steven Gray·Dominique Manchon
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Abstract

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.

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Kurusch Ebrahimi-Fard, W. Steven Gray, Dominique Manchon. 2016-03-18. Evaluating Generating Functions for Periodic Multiple Polylogarithms. https://doi.org/10.1007/978-3-030-37031-2_17

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