Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

Abstract

In this paper, we introduce a operator in order to derive a new generating functions of modified k − Pell numbers, Gaussian modified Pell numbers. By making use of the operator defined in this paper, we give some new generating functions for Bivariate Complex Fibonacci and Lucas Polynomials, modified Pell Polynomials and Gaussian modified Pell Polynomials.

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

“…In this contribution, we will define an operator denoted by 12 k aa  and the complete homogeneous symmetric function for which we can formulate, extends and proves results based on our previous ones [13,[15][16][17][18]. In order to determine 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.…”

Complete Homogeneous Symmetric Functions of Third and Second-Order Linear Recurrence Sequences Nabiha Saba, Ali Boussayoud and Abdelhamid Abderrezzak

“…Corollary 19 [19] For n ∈ N, the generating function of modified Pell numbers q n is given by 36) and (37), we obtain…”

k-BALANCING NUMBERS AND NEW GENERATING FUNCTIONS WITH SOME SPECIAL NUMBERS AND POLYNOMIALS

“…The aim of this paper is to determine some new generating functions related to kbalancing. The concept of generating functions has been studied by many authors in the literature (see examples [8][9][10][11][12]).…”