On Cauchy Numbers and Their Generalizations
GAZI UNIVERSITY JOURNAL OF SCIENCE, vol.33, no.2, pp.456-474, 2020 (ESCI, Scopus, TRDizin)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.