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A Generalization of Poly‐Cauchy Numbers and Their Properties

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  • Takao Komatsu
  • Vichian Laohakosol
  • Kálmán Liptai

Abstract

In Komatsu′s work (2013), 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.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:179841
DOI: 10.1155/2013/179841
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