Higher-Order Jacobsthal–Lucas Quaternions

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Uysal M., Özkan E.

Axioms, cilt.11, sa.12, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 12
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3390/axioms11120671
  • Dergi Adı: Axioms
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Jacobsthal-Lucas quaternions, higher-order Jacobsthal-Lucas quaternions, Binet formula
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Marmara Üniversitesi Adresli: Hayır

Özet

In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties. We give Binet’s formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, and exponential generating functions of the higher-order Jacobsthal–Lucas quaternions. We also give some relations between higher-order Jacobsthal and Jacobsthal–Lucas quaternions.