On Cauchy Numbers and Their Generalizations


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KARGIN L.

GAZI UNIVERSITY JOURNAL OF SCIENCE, vol.33, no.2, pp.456-474, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.35378/gujs.604550
  • Journal Name: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.456-474
  • Keywords: Cauchy numbers, Poly-Cauchy numbers, p-Cauchy numbers, Generating function, Recurrence relations, BERNOULLI NUMBERS, POLY-BERNOULLI
  • Akdeniz University Affiliated: Yes

Abstract

This paper is concerned with both kinds of the Cauchy numbers and their generalizations. Taking into account Mellin derivative, we relate p-Cauchy numbers of the second kind with shifted Cauchy numbers of the first kind, which yields new explicit formulas for the Cauchy numbers of the both kind. We introduce a generalization of the Cauchy numbers and investigate several properties, including recurrence relations, convolution identities and generating functions. In particular, these results give rise to new identities for Cauchy numbers.