Abstract: In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.

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Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials

The main aim of this paper is to introduce new concept of bivariate Mersenne Lucas polynomials { m n ( x , y ) } n = 0 ∞ , we first give the recurrence relation of them. We then obtain Binet’s formula, generating function, Catalan’s identity and Cassini’s identity for this type of polynomials. After that, we give the symmetric function, explicit formula and d’Ocagne’s identity of bivariate Mersenne and bivariate Mersenne Lucas polynomials. By using the Binet’s formula we obtain some well-known identities of these bivariate polynomials. Also, some summation formulas of bivariate Mersenne and bivariate Mersenne Lucas polynomials are investigated.

On the bivariate Mersenne Lucas polynomials and their properties

In this study, we introduce a new class of generating functions of odd and even Gaussian (p,q)-Fibonacci numbers, Gaussian (p,q)-Lucas numbers, Gaussian (p,q)-Pell numbers, Gaussian (p,q)-Pell Lucas numbers, Gaussian Jacobsthal numbers and Gaussian Jacobsthal Lucas numbers and we will recover the new generating functions of some Gaussian polynomials at odd and even terms. The technique used her is based on the theory of the so called symmetric functions.

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Generating functions of even and odd gaussian numbers and polynomials

In this paper, we introduce Mersenne and Mersenne-Lucas hybrinomial quaternions and present some of their properties. Some identities are derived for these polynomials. Furthermore, we give the Binet formulas, Catalan, Cassini, d’Ocagne identity and generating and exponential generating function of these hybrinomial quaternions.

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On the Mersenne and Mersenne-Lucas hybrinomial quaternions

This paper aims to introduce the k -Mersenne and k -Mersenne-Lucas octonions. We give the closed form formulae for these octonions and obtain some well-known identities like Cassini’s identity, d’Ocagne’s identity, Catalan identity, Vajda’s identity and generating functions of them. As a consequence k = 1 yields all the above properties for Mersenne and Mersenne-Lucas octonions.

On $k$-Mersenne and k-Mersenne-Lucas Octonions

In this paper, we will recover the generating functions of generalized polynomials of second order. The technic used her is based on the theory of the so called symmetric functions.

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Symmetric Functions of Generalized Polynomials of Second Order

In this paper, we will introduce a new definition of k-Mersenne–Lucas numbers and investigate some properties. Then, we obtain some identities and established connection formulas between k-Mersenne–Lucas numbers and k-Mersenne numbers through the use of Binet’s formula.

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On the k-Mersenne–Lucas numbers

In this paper, we introduce a new operator in order to derive some properties of homogeneous symmetric functions. By making use of the proposed operator, we give some new generating functions for Mersenne numbers, Mersenne numbers and product of sequences and Chebychev polynomials of second kind.

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On Some Identities and Generating Functions for Mersenne Numbers and Polynomials

In this paper, we will recover the new generating functions of some products of Tribonacci Lucas numbers and orthogonal polynomials. The technic used her is based on the theory of the so called symmetric functions.

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Symmetric functions of binary products of tribonacci lucas numbers and orthogonal polynomials

A bstract . In this paper, we will recover the generating functions of Tribonacci numbers and Chebychev polynomials of ﬁrst and second kind. By making use of the operator deﬁned in this paper, we give some new generating functions for the binary products of Tribonacci with some remarkable numbers and polynomials. The technique used here is based on the theory of the so-called symmetric functions.

Mourad Chelgham

Papers

Symmetric Functions of Generalized Polynomials of Second Order

On the k-Mersenne–Lucas numbers

On Some Identities and Generating Functions for Mersenne Numbers and Polynomials

Symmetric functions of binary products of tribonacci lucas numbers and orthogonal polynomials

A new class of symmetric functions of binary products of tribonacci numbers and other well-known numbers