On the Bicomplex $k$-Fibonacci Quaternions

Abstract

In this paper, bicomplex $k$-Fibonacci quaternions are defined. Also, some algebraic properties of bicomplex $k$-Fibonacci quaternions are investigated. For example, the summation formula, generating functions, Binet's formula, the Honsberger identity, the d'Ocagne's identity, Cassini's identity, Catalan's identity for these quaternions are given. In the last part, a different way to find $n-th$ term of the bicomplex $k$-Fibonacci quaternion sequence was given using the determinant of a tridiagonal matrix.

Keywords

• bicomplex number
• k-fibonacci number
• bicomplex fibonacci quaternion
• bicomplex k-fibonacci quaternion
• tridiagonal matrix