scholarly journals Symmetric functions of binary products of fibonacci and orthogonal polynomials

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1495-1504 ◽  
Author(s):  
Ali Boussayoud ◽  
Mohamed Kerada ◽  
Serkan Araci ◽  
Mehmet Acikgoz ◽  
Ayhan Esi
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Symmetric Functions ◽  
Fibonacci Numbers ◽  
Chebychev Polynomials ◽  
Symmetric Properties

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

SYMMETRIC FUNCTIONS OF BINARY PRODUCTS OF TRIBONACCI LUCAS NUMBERS AND ORTHOGONAL POLYNOMIALS

2021 ◽  
Vol 21 (2) ◽  
pp. 461-478
Author(s):  
HIND MERZOUK ◽  
ALI BOUSSAYOUD ◽  
MOURAD CHELGHAM
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Symmetric Functions ◽  
Lucas Numbers

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.

scholarly journals Construction of a new class of generating functions of binary products of some special numbers and polynomials

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 1001-1013
Author(s):  
Souhila Boughaba ◽  
Ali Boussayoud ◽  
Serkan Araci ◽  
Mohamed Kerada ◽  
Mehmet Acikgoz
Keyword(s):  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Fibonacci Numbers ◽  
Fibonacci Polynomials ◽  
Pell Numbers ◽  
New Class ◽  
Special Numbers And Polynomials ◽  
Symmetric Properties

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.

scholarly journals GENERATING FUNCTIONS OF EVEN AND ODD GAUSSIAN NUMBERS AND POLYNOMIALS

2021 ◽  
Vol 21 (1) ◽  
pp. 125-144
Author(s):  
NABIHA SABA ◽  
ALI BOUSSAYOUD ◽  
MOHAMED KERADA
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Fibonacci Numbers ◽  
Lucas Numbers ◽  
Pell Numbers ◽  
New Class ◽  
Gaussian Polynomials

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.

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

2020 ◽  
pp. 2150031
Author(s):  
Ali Boussayoud ◽  
Mohamed Kerada ◽  
Serkan Araci ◽  
Mehmet Acikgoz
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Lucas Numbers ◽  
Fibonacci Polynomials ◽  
Pell Numbers ◽  
Symmetric Properties

In this paper, we introduce a new operator in order to derive some new symmetric properties of [Formula: see text]-Fibonacci and [Formula: see text]-Lucas numbers and Fibonacci polynomials. By making use of the new operator defined in this paper, we give some new generating functions for [Formula: see text]-Fibonacci and Pell numbers and Fibonacci polynomials.

scholarly journals Symmetric Functions for k-Fibonacci Numbers and Orthogonal Polynomials

2018 ◽  
Vol 6 (3) ◽  
pp. 98-102
Author(s):  
Khadidja Boubellouta ◽  
Ali Boussayoud ◽  
Mohamed Kerada
Keyword(s):  
Orthogonal Polynomials ◽  
Symmetric Functions ◽  
Fibonacci Numbers

scholarly journals Generating Functions for Orthogonal Polynomials of A2, C2 and G2

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 354 ◽  
Author(s):  
Tomasz Czyżycki ◽  
Jiří Hrivnák ◽  
Jiří Patera
Keyword(s):  
Orthogonal Polynomials ◽  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Bell Polynomials ◽  
The Third ◽  
Weight Lattice ◽  
Hybrid Character ◽  
Polynomial Family

The generating functions of fourteen families of generalized Chebyshev polynomials related to rank two Lie algebras A 2 , C 2 and G 2 are explicitly developed. There exist two classes of the orthogonal polynomials corresponding to the symmetric and antisymmetric orbit functions of each rank two algebra. The Lie algebras G 2 and C 2 admit two additional polynomial collections arising from their hybrid character functions. The admissible shift of the weight lattice permits the construction of a further four shifted polynomial classes of C 2 and directly generalizes formation of the classical univariate Chebyshev polynomials of the third and fourth kinds. Explicit evaluating formulas for each polynomial family are derived and linked to the incomplete exponential Bell polynomials.

scholarly journals Combinatorial Expansions in $K$-Theoretic Bases

10.37236/2320 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Jason Bandlow ◽  
Jennifer Morse
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Schur Functions ◽  
Geometric Information ◽  
Combinatorial Description ◽  
Littlewood Polynomials ◽  
Stanley Symmetric Functions ◽  
K Theory ◽  
Combinatorial Representation

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape.  Included in this class are the Hall-Littlewood polynomials, $k$-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur functions represent the cohomology of the Grassmannian variety of $GL_n$, Grothendieck functions $\{G_\lambda\}$ represent the $K$-theory of the same space.  In this paper, we give a combinatorial description of the coefficients when any element of $\mathcal C$ is expanded in the $G$-basis or the basis dual to $\{G_\lambda\}$.

scholarly journals On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers

2020 ◽  
Vol 12 (2) ◽  
pp. 280-286
Author(s):  
Carlos M. da Fonseca
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Tridiagonal Matrices

AbstractIn this note, we recall several connections between the determinant of some tridiagonal matrices and the orthogonal polynomials allowing the relation between Chebyshev polynomials of second kind and Fibonacci numbers. With basic transformations, we are able to recover some recent results on this matter, bringing them into one place.

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