  In this study, we first provide some new theorems by using the symmetrizing
operator. After that, by using this theorems we introduce a new family of
generating functions of odd and even terms 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. Then, we give the
new generating functions of the products of these (p,q)-numbers with odd and
even phrases of (p,q)-numbers.

Number Theory