Bicomplex k-Fibonacci quaternions

TL;DR

This paper introduces bicomplex k-Fibonacci quaternions, explores their algebraic properties, and derives several identities connecting them with bicomplex numbers and k-Fibonacci numbers.

Contribution

It defines bicomplex k-Fibonacci quaternions and investigates their algebraic properties and identities, expanding the mathematical understanding of these combined structures.

Findings

Derived Honsberger, d'Ocagne's, Binet's, Cassini's, and Catalan's identities for bicomplex k-Fibonacci quaternions.

Established algebraic properties linking bicomplex numbers and k-Fibonacci numbers.

Provided formulas and identities that extend classical Fibonacci identities to bicomplex quaternions.

Abstract

In this paper, bicomplex k-Fibonacci quaternions are defined. Also, some algebraic properties of bicomplex k-Fibonacci quaternions which are connected with bicomplex numbers and k-Fibonacci 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.