On The Horadam Hybrid Quaternions
Ali Da\u{g}deviren, Ferhat K\"ur\"uz
TL;DR
This paper introduces the Horadam hybrid quaternions, explores their properties, and establishes relationships with Fibonacci and Lucas hybrid quaternions, including formulas and identities.
Contribution
It defines the new class of Horadam hybrid quaternions and derives their fundamental properties and relations to existing Fibonacci and Lucas hybrid quaternions.
Findings
Derived Binet formulas for these quaternions
Established Cassini identities for the new quaternions
Connected Fibonacci and Lucas hybrid quaternions through these properties
Abstract
In this paper, we define the Horadam hybrid quaternions and give some of their properties. Moreover, we investigate the relations between the Fibonacci hybrid quaternions and the Lucas hybrid quaternions which connected the Fibonacci quternions and Lucas quaternions. Furthermore, we give the Binet formulas and Cassini identities for these quaternions.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematics and Applications · Algebraic and Geometric Analysis