Ordinary Generating Functions for Second-Order Recurrence Sequences.

Abstract

In this dissertation, we present a theorem in order to calculate new generating functions for second-order recurrences relations. The presented theorem is based on symmetric functions. Where by making use the symmetrizing operator kc 1c2 kb1b2 on the series X1 n=0 Sn(A)bn1 cn1 zn we gived the generating functions of the products of Fibonacci numbers, Pell numbers and Jacobsthal numbers with the bivariate Fibonacci polynomials, bivariate Lucas polynomial, bivariate Pell Lucas polynomials, bivariate Jacobsthal and Jacobsthal Lucas polynomials