Abstract
We give some formulas of poly-Cauchy numbers by the r-Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are with Stirling numbers of the first kind. In our case of the classical or poly-Cauchy numbers, the formulas are with Stirling numbers of the second kind. We also discuss annihilation formulas for poly-Cauchy number with negative indices.
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The author thanks the anonymous referee for careful reading of the manuscript and making useful comments from a broader perspective.
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Komatsu, T. Recurrence Relations of Poly-Cauchy Numbers by the r-Stirling Transform. Mediterr. J. Math. 19, 37 (2022). https://doi.org/10.1007/s00009-021-01960-w
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DOI: https://doi.org/10.1007/s00009-021-01960-w