On Higher Order Lucas Hybrid Quaternions

Aydın F. T.

Konuralp Journal of Mathematics, vol.12, no.1, pp.46-54, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2024
  • Journal Name: Konuralp Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.46-54
  • Keywords: Binet formula, Exponential generating function, Fibonacci number, Generating function, Higher order Fibonacci number, Higher order Lucas number, Hybrid number, Lucas number
  • Yıldız Technical University Affiliated: Yes

Abstract

In this article, we introduced higher order Lucas hybrid quaternions with the help of higher order Lucas numbers. We also examined some algebraic properties of these quaternions. By obtaining the recurrence relation, we found the Binet formula, the generating function and the exponential generating function. Finally, we calculated the Vajda identity for the higher order Lucas hybrid quaternions and obtained the Catalan, Cassini and d’Ocagne identities with the help of this identity.