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<p>It is known that the directional limit values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the reverse 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月27日

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  • Yoni Ishii,
  • Takeshi Shinohara

摘要

It is known that the directional limit values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the reverse 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.