Construction of dual-generalized complex Fibonacci and Lucas quaternions

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.

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How to Cite
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Şentürk G., Gürses N., Yüce S. Construction of Dual-Generalized Complex Fibonacci and Lucas Quaternions. Carpathian Math. Publ. 2022, 14 (2), 406-418.