Some recurrence relations of poly-Cauchy numbers

Volume 12, Issue 12, pp 829--845 http://dx.doi.org/10.22436/jnsa.012.12.05

Publication Date: August 07, 2019 Submission Date: June 01, 2019 Revision Date: July 01, 2019 Accteptance Date: July 23, 2019

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Authors

Takao Komatsu - Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China.

Abstract

Poly-Cauchy numbers \(c_n^{(k)}\) (\(n\ge 0\), \(k\ge 1\)) have explicit expressions in terms of the Stirling numbers of the first kind. When the index is negative, there exists a different expression. However, the sequence \(\{c_n^{(-k)}\}_{n\ge 0}\) seem quite irregular for a fixed integer \(k\ge 2\). In this paper we establish a certain kind of recurrence relations among the sequence \(\{c_n^{(-k)}\}_{n\ge 0}\), analyzing the structure of poly-Cauchy numbers. We also study those of poly-Cauchy numbers of the second kind, poly-Euler numbers, and poly-Euler numbers of the second kind. Some different proofs are given. As applications, some leaping relations are shown.

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ISRP Style

Takao Komatsu, Some recurrence relations of poly-Cauchy numbers, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 12, 829--845

AMA Style

Komatsu Takao, Some recurrence relations of poly-Cauchy numbers. J. Nonlinear Sci. Appl. (2019); 12(12):829--845

Chicago/Turabian Style

Komatsu, Takao. "Some recurrence relations of poly-Cauchy numbers." Journal of Nonlinear Sciences and Applications, 12, no. 12 (2019): 829--845

Keywords

Poly-Cauchy numbers
poly-Euler numbers
recurrence
leaping relations
Vandermonde's determinant

MSC

11B75
11B37
11B68
11B73
05A19
11C20
15A15

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