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arXiv · 2508.12577

Stirling polynomials and multiple zeta (star) functions at non-positive integers

Yoni Ishii·Takeshi Shinohara
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Abstract

It is known that the values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the values of MZFs and multiple zeta star functions (MZSFs) at non-positive integers using Stirling polynomials. We also study the following two points: a connection between MZFs and MZSFs at non-positive integers and a connection between reverse values and generalized Gregory coefficients studied by Matsusaka, Murahara, and Onozuka.

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Yoni Ishii, Takeshi Shinohara. 2025-08-18. Stirling polynomials and multiple zeta (star) functions at non-positive integers. https://arxiv.org/abs/2508.12577

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