Dual-complex k-Pell quaternions
F\"ugen Torunbalc{\i} Ayd{\i}n
TL;DR
This paper introduces dual-complex k-Pell quaternions, explores their algebraic properties, and derives several classical identities adapted to these new mathematical objects.
Contribution
It defines dual-complex k-Pell quaternions and investigates their properties, extending classical identities to this new quaternionic framework.
Findings
Derived algebraic properties of dual-complex k-Pell quaternions
Established identities such as Honsberger, d'Ocagne's, Binet's, Cassini's, Catalan's for these quaternions
Connected properties with dual-complex numbers and k-Pell numbers
Abstract
In this paper, dual-complex k-Pell numbers and dual-complex k-Pell quaternions are defined. Also, some algebraic properties of dual-complex k-Pell numbers and quaternions which are connected with dual-complex numbers and k-Pell numbers are investigated. Furthermore, the Honsberger identity, the d'Ocagne's identity, Binet's formula, Cassini's identity, Catalan's identity for these quaternions are given.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Algebraic and Geometric Analysis · Mathematics and Applications