On Quaternions with Higher Order Jacobsthal Numbers Components

Creative Commons License

ÖZKAN E., UYSAL M.

Gazi University Journal of Science, vol.36, no.1, pp.336-347, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.35378/gujs.1002454
  • 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, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.336-347
  • Keywords: Binet formula, Exponential generating functions, Higher order Jacobsthal numbers, Higher order Jacobsthal quaternions
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions.