Construction of dual-generalized complex Fibonacci and Lucas quaternions

G.Y. Şentürk; N. Gürses; S. Yüce

doi:10.15330/cmp.14.2.406-418

G.Y. Şentürk Istanbul Gelişim University, 34310, Istanbul, Türkiye https://orcid.org/0000-0002-8647-1801
N. Gürses Yildiz Technical University, 34220, Istanbul, Türkiye https://orcid.org/0000-0001-8407-854X
S. Yüce Yildiz Technical University, 34220, Istanbul, Türkiye https://orcid.org/0000-0002-8296-6495

https://doi.org/10.15330/cmp.14.2.406-418

Keywords: quaternion, dual-generalized complex number, Fibonacci number, Lucas number

Published online: 2022-11-21

Abstract

The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger's, d'Ocagne's, Cassini's and Catalan's identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fibonacci and Lucas quaternions are also expressed as their different matrix representations.