ORDINARY GENERATING FUNCTIONS OF BINARY PRODUCTS OF (p,q)-MODIFIED PELL NUMBERS AND k-NUMBERS AT POSITIVE AND NEGATIVE INDICES

Abstract

In this paper, we introduce a operator in order to derive some new symmetric properties of (p,q)-modified Pell numbers and we give some new generating functions of the products of (p,q)-modified Pell numbers with k-Fibonacci and k-Lucas numbers, k-Pell and k-Pell Lucas numbers, k-Jacobsthal and k-Jacobsthal Lucas numbers at positive and negative indices. By making use of the operator defined in this paper, we give some new generating functions of the products of (p,q)-modified Pell numbers with k-balancing and k-Lucas-balancing numbers.