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arXiv · 2601.17539

Laurent type expansion of multiple polylogarithms at integer points

Pawan Singh Mehta·Biswajyoti Saha
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Abstract

In this article, we study the local behaviour of the multiple polylogarithm functions at integer points, in the $s$-aspect. This is done by writing a Laurent type expansion at integer points, involving certain power series and rational functions. The coefficients of these power series are the regularised values of the multiple polylogarithm functions at certain related integer points.

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Pawan Singh Mehta, Biswajyoti Saha. 2026-01-24. Laurent type expansion of multiple polylogarithms at integer points. https://arxiv.org/abs/2601.17539

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