Abstract
The integer values of Cauchy polynomials are expressed in terms of \({r}\)-Stirling numbers of the first kind. Several relations between the integral values of Bernoulli polynomials and those of Cauchy polynomials are obtained in terms of \({r}\)-Stirling numbers of both kinds. Also, we find a relation between the Cauchy polynomials and hyperharmonic numbers.
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The first author was supported in part by the grant of Wuhan University and by the grant of Hubei Provincial Experts Program.
The second author was supported by the Scientific Research Foundation of Nanjing University of Information Science & Technology, The Startup Foundation for Introducing Talent of NUIST, Project no.: S8113062001, and the National Natural Science Foundation for China. Grant no. 11501299.
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Komatsu, T., Mező, I. Several explicit formulae of Cauchy polynomials in terms of \({r}\)-Stirling numbers. Acta Math. Hungar. 148, 522–529 (2016). https://doi.org/10.1007/s10474-016-0592-3
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DOI: https://doi.org/10.1007/s10474-016-0592-3