On the <i>k</i> -Lucas Numbers and Lucas Polynomials

Abstract

In this paper, we introduce an operator in order to derive some new symmetric properties of -Lucas numbers and Lucas polynomials. By making use of the operator defined in this paper, we give some new generating functions for -Lucas numbers and Lucas polynomials.

Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

“…These numbers are examples of a numbers defined by a recurrence relation of second order. It is well known that the modified k − Pell numbers { } , N k n n q ∈ is defined in [1] [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In order to determine generating functions of modified k-Pell numbers, Gaussian modified Pell numbers, Bivariate Complex Fibonacci and Lucas Polynomials, modified Pell Polynomials and Gaussian modified Pell Polynomials, we use analytical means and series manipulation methods.…”

Symmetric Functions for <i>k</i>-Fibonacci Numbers and Orthogonal Polynomials

“…The main purpose of this paper is to present some results involving the k-Fibonacci and k-Jacobsthal numbers using define a new useful operator denoted by δ By making use of this operator, we can derive new results based on our previous ones [8,9,10,11,12]. In order to determine generating functions of the product of k-Fibonacci and k-Jacobsthal numbers and Chebychev polynomials of second kind, we combine between our indicated past techniques and these presented polishing approaches.…”

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

“…In this part, we now derive the new generating functions of the products of some known numbers. For the applications of generating functions of some known functions, we refer the reader to see the references [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. For the case A = {a 1 , −a 2 } and E = {e 1 , −e 2 } with replacing a 2 by −a 2 , e 2 by −e 2 in (3.1), we have…”