多柯西数的一些递推关系

Journal of Nonlinear Sciences and Applications Pub Date : 2019-08-07 DOI:10.22436/JNSA.012.12.05

T. Komatsu

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引用次数: 2

摘要

聚柯西数cn (n > 0, k > 1)有第一类斯特林数的显式表达式。当指数为负时，存在不同的表达式。然而，对于一个固定的整数k > 2来说，序列{c n}n>0似乎非常不规则。本文建立了序列{c n}n>0之间的一类递推关系，分析了多柯西数的结构。我们还研究了第二类聚柯西数、第二类聚欧拉数和第二类聚欧拉数。给出了一些不同的证明。作为应用，给出了一些跳跃关系。

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Some recurrence relations of poly-Cauchy numbers

Poly-Cauchy numbers c n (n > 0, k > 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 }n>0 seem quite irregular for a fixed integer k > 2. In this paper we establish a certain kind of recurrence relations among the sequence {c n }n>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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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

自引率

0.00%

发文量

期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.