On Higher Order Lucas Hybrid Quaternions

Year 2024, Volume: 12 Issue: 1, 46 - 54, 30.04.2024

Fügen Torunbalcı Aydın

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.

Keywords

Fibonacci number, Lucas number, Hybrid number, Higher order Lucas number, Binet formula

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