On Quaternions with Higher Order Jacobsthal Numbers Components

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ÖZKAN E., UYSAL M.

Gazi University Journal of Science, cilt.36, sa.1, ss.336-347, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.35378/gujs.1002454
  • 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, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.336-347
  • Anahtar Kelimeler: Binet formula, Exponential generating functions, Higher order Jacobsthal numbers, Higher order Jacobsthal quaternions
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

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.