On the properties of k-balancing numbers

Abstract

In this study, a generalization of the sequence of balancing numbers called as k-balancing numbers is considered and some of their properties are established. Further, the balancing polynomials that are the natural extension of k-balancing numbers are presented and observe that many of their properties admit straightforward proofs. The derivatives of these polynomials in the form of convolution are also discussed. Keywords: Balancing numbers, Balancers, k-Balancing numbers, Balancing polynomials