A new family of symmetric and generating functions of binary products of (p,q)-numbers at consecutive and nonconsecutive terms

Abstract

In this study, by making use of the symmetrizing operator δ_{a₁a₂}^{k+1} we introduce a new theorem. By using this theorem we give a new class of generating functions of the products of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q)-Jacobsthal numbers and (p,q)-Jacobsthal Lucas numbers at consecutive and nonconsecutive terms and the products of these (p,q)-numbers with Mersenne numbers at consecutive and nonconsecutive terms.