Journal ArticleDOI
On the bivariate Mersenne Lucas polynomials and their properties
Nabiha Saba,Ali Boussayoud +1 more
TLDR
In this article, a new concept of bivariate Mersenne Lucas polynomials is introduced and the recurrence relation of them is given, and Binet's formula, generating function, Catalan's identity and Cassini's identity for this type of polynomial are obtained.Abstract:
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.read more
Citations
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A novel chaos based generating function of the Chebyshev polynomials and its applications in image encryption
TL;DR: The bifurcation diagram and Lyapunov exponent proved that the proposed generating function for Chebyshev polynomials is a deterministic system that exhibits chaotic behavior for specific values of the control parameters.
Journal ArticleDOI
Generating functions of binary products of (p,q)-Fibonacci-like numbers with odd and even certain numbers and polynomials
Nabiha Saba,Ali Boussayoud +1 more
TL;DR: In this paper , the symmetric and generating functions for odd and even terms of second-order linear recurrence sequences were studied and a new family of generating functions of odd terms of (p,q)-Fibonacci-like numbers and polynomials were derived.
Journal ArticleDOI
On the generalized Fibonacci like sequences and matrices
Kalika Prasad,Hrishikesh Mahato +1 more
TL;DR: In this article , the generalized Fibonacci-like sequences with arbitrary initial seed were studied and various properties of these generalized sequences, including properties of the identity matrix and its relation with the Lucas numbers and the trace sequence of the original trace.
Gaussian Mersenne Lucas numbers and polynomials
Nabiha Saba,Ali Boussayoud +1 more
TL;DR: In this paper , the authors introduce three new notions called Gaussian Mersenne Lucas numbers (GMML) which are called MERSenne Lucas polynomials, and prove their properties such as recurrence relations, Binet's formulas, explicit formulas, generating functions, symmetric functions and negative extensions.
References
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Journal ArticleDOI
Symmetric and generating functions
Ali Boussayoud,Mohamed Kerada +1 more
TL;DR: In this paper, generalized symmetric functions are used to find explicit formulas of the Fibonacci numbers, and of the Tchebychev polynomials of first and second kinds.
On the Mersenne sequence
TL;DR: From Binet’s formula of Mersenne sequence, some properties for this sequence are obtained such as the generating matrix, tridiagonal matrices and circulant type matrices.
Posted Content
Some formulae for bivariate Fibonacci and Lucas polynomials
TL;DR: In this paper, a collection of identities for bivariate Fibonacci and Lucas polynomials using essentially a matrix approach as well as properties of such polynomorphials when the variables $x$ and $y$ are replaced by polynomial coefficients was derived.
Posted Content
Generalized bivariate Fibonacci polynomials
TL;DR: In this article, generalized bivariate polynomials are derived from the initial conditions of the bivariate Fibonacci polynomial and Lucas polynomorphism, and identities and inequalities are derived using essentially a matrix approach.
Journal ArticleDOI
Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials
Nabiha Saba,Ali Boussayoud +1 more
TL;DR: In this article, a symmetric function was introduced in order to derive a new generating function of bivariate Pell Lucas polynomials, and complete homogeneous symmetric functions were defined for Gauss Fibonacci, Gauss Lucas, and Jacobsthal Lucas poynomials.