Geodesic
Some recurrence relations of poly-Cauchy numbers
Komatsu, Takao 1
1 Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 829-845.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.012.12.05
Classification : 11B75, 11B37, 11B68, 11B73, 05A19, 11C20, 15A15
Keywords: Poly-Cauchy numbers, poly-Euler numbers, recurrence, leaping relations, Vandermonde's determinant

Komatsu, Takao  1

1 Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China 
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Komatsu, Takao . Some recurrence relations of poly-Cauchy numbers. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 829-845. doi : 10.22436/jnsa.012.12.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.12.05/

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