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<p>In this paper, we will describe a recursive formula of multiple Eulerian polynomials and then we prove that all roots of these polynomials are negative real numbers. On the other hand, extending Euler’s techniques to calculate the zeta values at negative indices, we also give a new way to regularize the polyzetas at nonpositive integer multi-indices.</p>

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Multiple Eulerian polynomials

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Ta Thi Hoai An,
  • Ngo Quoc Hoan

摘要

In this paper, we will describe a recursive formula of multiple Eulerian polynomials and then we prove that all roots of these polynomials are negative real numbers. On the other hand, extending Euler’s techniques to calculate the zeta values at negative indices, we also give a new way to regularize the polyzetas at nonpositive integer multi-indices.