Symmetric functions of the k-Fibonacci and k-Lucas numbers

In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Lucas numbers and Fibonacci polynomials. By making use of the new operator defined in this paper, we give some new generating functions for k-Fibonacci and Pell numbers and Fibonacci polynomials. © 2020 World Scientific Publishing Company

Generating functions of binary products of k-Fibonacci and orthogonal polynomials

In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Pell numbers and Tchebychev polynomials of first and second kind. By making use of the new operator defined in this paper, we give some new generating functions for k-Fibonacci and k-Pell numbers and Fibonacci polynomials

Construction of a new class of symmetric function of binary products of (p, q)-numbers with 2-orthogonal Chebyshev polynomials

In this paper, we give some new 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 with 2-orthogonal Chebyshev polynomials and trivariate Fibonacci polynomials. © 2021, Sociedad Matemática Mexicana

Generating Functions of the Products of Bivariate Complex Fibonacci Polynomials with Gaussian Numbers and Polynomials

In this paper, we define and study the bivariate complex Fibonacci and Lucas polynomials. We introduce a operator in order to derive some new symmetric properties of bivariate complex Fibonacci and bivariate complex Lucas polynomials, and give the generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Fibonacci, Gaussian Lucas and Gaussian Jacobsthal numbers, Gaussian Pell numbers, Gaussian Pell Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Jacobsthal, Gaussian Jacobsthal Lucas polynomials and Gaussian Pell polynomials

A new class of ordınary generatıng functıons for bınary products of mersenne numbers and gaussıan numbers wıth parameters p and q

In this paper, we derive some new generating functions for the products of several special numbers including (p, q)-Fibonacci numbers, (p, q)-modified Pell numbers, and (p, q)-Jacobsthal Lucas numbers. We also give some new generating functions for the products of Mersenne and Gaussian numbers with parameters p and q. © 2023, Colgate University. All rights reserved

Construction of a New Class of Generating Functions of Binary Products of Some Special Numbers and Polynomials

In this paper, we derive some new symmetric properties of k-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special numbers such as k-Fibonacci numbers, k-Pell numbers, Jacobsthal numbers, Fibonacci polynomials and Chebyshev polynomials