Some Properties of Hyperbolic k-Narayana Quaternions

Abstract

In this paper, we introduced the hyperbolic k-Narayana quaternions. Several properties of these quaternions are investigated, including the Binet formulas, generating functions, and summation formulas. Moreover, some identities such as Catalan, Cassini, and d’Ocagne are obtained. Our results extend and generalize well-known theorems.