A New Hybrid Generalization of Balancing Polynomials

Abstract

In this paper, we introduce and study balancing hybrinomials, i.e., polynomials being a generalization of balancing hybrid numbers. We provide some properties of the balancing hybrinomials, including Catalan, Cassini, d’Ocagne, and Vajda identities, among others. Moreover, we present a matrix representation of the hybrinomials.

Keywords

• balancing numbers
• complex numbers
• hyperbolic numbers
• dual numbers
• polynomials
• Diophantine equations