On Cauchy Numbers and Their Generalizations

Creative Commons License

KARGIN L.

GAZI UNIVERSITY JOURNAL OF SCIENCE, cilt.33, sa.2, ss.456-474, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.35378/gujs.604550
  • Dergi Adı: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: 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)
  • Sayfa Sayıları: ss.456-474
  • Anahtar Kelimeler: Cauchy numbers, Poly-Cauchy numbers, p-Cauchy numbers, Generating function, Recurrence relations, BERNOULLI NUMBERS, POLY-BERNOULLI
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.