A generalization of poly-Cauchy numbers and their properties
type: Item
instance of: scholarly article
title: A generalization of poly-Cauchy numbers and their properties
zbMATH Open document ID: 1295.11025
DOI: 10.1155/2013/179841
author: Takao Komatsu
author: Vichian Laohakosol
author: Kálmán Liptai
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: In the first author's work [Kyushu J. Math. 67, No. 1, 143--153 (2013; Zbl 1295.11024)], the concept of poly-Cauchy numbers is introduced as an analogue of that of poly-Bernoulli numbers. Both numbers are extensions of classical Cauchy numbers and Bernoulli numbers, respectively. There are several generalizations of poly-Cauchy numbers, including poly-Cauchy numbers with a \(q\) parameter and shifted poly-Cauchy numbers. In this paper, we give a further generalization of poly-Cauchy numbers and investigate several arithmetical properties. We also give the corresponding generalized poly-Bernoulli numbers so that both numbers have some relations.
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 6306106
zbMATH Keywords: poly-Cauchy number
zbMATH Keywords: poly-Bernoulli number
zbMATH Keywords: Stirling number
Wikidata QID: Q58915458
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/179841
OpenAlex ID: W2097737486
cites work: Poly-Cauchy numbers
cites work: Q4769056
cites work: The Cauchy numbers
cites work: Q4320535
cites work: Q4443440
cites work: Poly-Bernoulli numbers
cites work: Poly-Cauchy numbers with a \(q\) parameter
cites work: Shifted poly-Cauchy numbers
cites work: Some relationships between poly-Cauchy numbers and poly-Bernoulli numbers
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description: scientific article; zbMATH DE number 6306106