scholarly journals A basic class of symmetric orthogonal polynomials using the extended Sturm–Liouville theorem for symmetric functions

2007 ◽  
Vol 325 (2) ◽  
pp. 753-775 ◽  
Author(s):  
Mohammad Masjed-Jamei
Keyword(s):  
Orthogonal Polynomials ◽  
Symmetric Functions ◽  
Liouville Theorem ◽  
Basic Class ◽  
Sturm Liouville

scholarly journals On the analytic form of the discrete Kramer sampling theorem

2001 ◽  
Vol 25 (11) ◽  
pp. 709-715 ◽  
Author(s):  
Antonio G. García ◽  
Miguel A. Hernández-Medina ◽  
María J. Muñoz-Bouzo
Keyword(s):  
Orthogonal Polynomials ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Form ◽  
Sampling Theorem ◽  
Discrete Version ◽  
Moment Problems ◽  
Sturm Liouville ◽  
The Subject ◽  
Sampling Expansions

The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems. In this paper a discrete version of the analytic Kramer sampling theorem is proved. Orthogonal polynomials arising from indeterminate Hamburger moment problems as well as polynomials of the second kind associated with them provide examples of Kramer analytic kernels.

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 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.

Diophantine equations for Morgan-Voyce and other modified orthogonal polynomials

2008 ◽  
Vol 58 (1) ◽  
Author(s):  
Thomas Stoll ◽  
Robert Tichy
Keyword(s):  
Orthogonal Polynomials ◽  
Liouville Equation ◽  
Diophantine Equation ◽  
Diophantine Equations ◽  
Second Order ◽  
Recurrence Equation ◽  
Classical Orthogonal Polynomials ◽  
The Third ◽  
Sturm Liouville

AbstractIt is well-known that Morgan-Voyce polynomials B n(x) and b n(x) satisfy both a Sturm-Liouville equation of second order and a three-term recurrence equation ([SWAMY, M.: Further properties of Morgan-Voyce polynomials, Fibonacci Quart. 6 (1968), 167–175]). We study Diophantine equations involving these polynomials as well as other modified classical orthogonal polynomials with this property. Let A, B, C ∈ ℚ and {pk(x)} be a sequence of polynomials defined by $$\begin{gathered} p_0 (x) = 1 \hfill \\ p_1 (x) = x - c_0 \hfill \\ p_{n + 1} (x) = (x - c_n )p_n (x) - d_n p_{n - 1} (x), n = 1,2,..., \hfill \\ \end{gathered} $$ with $$(c_0 ,c_n ,d_n ) \in \{ (A,A,B),(A + B,A,B^2 ),(A,Bn + A,\tfrac{1}{4}B^2 n^2 + Cn)\} $$ with A ≠ 0, B > 0 in the first, B ≠ 0 in the second and C > −¼B 2 in the third case. We show that the Diophantine equation with m > n ≥ 4, ≠ 0 has at most finitely many solutions in rational integers x, y.

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