On Balancing Quaternions and Lucas-Balancing Quaternions

Abstract

In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have been obtained for these quaternions.

Keywords

• balancing number
• lucas-balancing number
• quaternion
• binet formula
• generating function
• 11r52
• 11b37