On dual hyperbolic numbers with generalized Jacobsthal numbers components


SOYKAN Y., TAŞDEMİR E., OKUMUŞ İ.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, vol.54, no.3, pp.824-840, 2023 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 54 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1007/s13226-022-00301-1
  • Journal Name: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Page Numbers: pp.824-840
  • Keywords: Jacobsthal numbers, Jacobsthal-Lucas numbers, Dual hyperbolic numbers, Dual hyperbolic Jacobsthal numbers, Cassini identity, PELL
  • Istanbul University-Cerrahpasa Affiliated: Yes

Abstract

In this paper, we introduce the generalized dual hyperbolic Jacobsthal numbers. As special cases, we deal with dual hyperbolic Jacobsthal and dual hyperbolic Jacobsthal-Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesaro's, Melham's identities and present matrices related with these sequences.