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New Identities Involving Cauchy Numbers, Harmonic Numbers and Zeta Values

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Abstract

In this article, we present a class of identities linking together Cauchy numbers, the special values of the Riemann zeta function and its derivative, and a generalization of the Roman harmonic numbers, which represents a significant refinement and improvement of our earlier work on the subject.

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Notes

  1. If \(b(n) = \frac{1}{n} \sum _{j=1}^n (-1)^{j-1} \left( {\begin{array}{c}n\\ j\end{array}}\right) j\,a(j)\), then \(a(n) = \frac{1}{n} \sum _{j=1}^n (-1)^{j-1} \left( {\begin{array}{c}n\\ j\end{array}}\right) j \, b(j)\) (cf. [5, Definition 5 and Corollary 1]).

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  1. CNRS, LJAD (UMR 7351), Université Côte d’Azur, Nice, France

    Marc-Antoine Coppo

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  1. Marc-Antoine Coppo
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Correspondence to Marc-Antoine Coppo.

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Coppo, MA. New Identities Involving Cauchy Numbers, Harmonic Numbers and Zeta Values. Results Math 76, 189 (2021). https://doi.org/10.1007/s00025-021-01497-0

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