On The Q - Seidel Matrix

Abstract

Clarke and et. al recently introduced the q-Seidel matrix, and obtained some properties. In this article, we define a different form of q-Seidel matrix by a(n)(k) (x, q) = xq(n+2k-3)a(n)(k-1) (x, q)+an(k-1)(x, q)+a(n+1)(k-1) with k >= 1, n >= 0 for an initial sequence a(n)(0) (x, q) = a(n) (x, q). By using our definition, we obtain several properties of the q-analogues of generalized Fibonacci and Lucas polynomials.