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A Generalization of Poly-Cauchy Numbers and Their Properties

Author

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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.

Suggested Citation

  • Takao Komatsu & Vichian Laohakosol & Kálmán Liptai, 2013. "A Generalization of Poly-Cauchy Numbers and Their Properties," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    • Handle: RePEc:hin:jnlaaa:179841
    DOI: 10.1155/2013/179841
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    Cited by:

    1. Noel Lacpao & Roberto Corcino & Mary Ann Ritzell Vega, 2019. "Hurwitz-Lerch Type Multi-Poly-Cauchy Numbers," Mathematics, MDPI, vol. 7(4), pages 1-11, April.
    2. Bényi, Beáta & Méndez, Miguel & Ramírez, José L. & Wakhare, Tanay, 2019. "Restricted r-Stirling numbers and their combinatorial applications," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 186-205.

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