Results 11 to 20 of about 411,141 (342)
Characterizations of classical orthogonal polynomials on quadratic lattices [PDF]
arXiv, 2016 This paper is devoted to characterizations classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials on quadratic lattices. Moreover a new characterization is also presented.
Marlyse Njinkeu Sandjon +3 more
arxiv +5 more sources
The Laguerre Constellation of Classical Orthogonal Polynomials
MathematicsA linear functional u is classical if there exist polynomials ϕ and ψ with degϕ≤2 and degψ=1 such that Dϕ(x)u=ψ(x)u, where D is a certain differential, or difference, operator. The polynomials orthogonal with respect to the linear functional u are called classical orthogonal polynomials.
Roberto S. Costas-Santos
doaj +5 more sources
d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only systems on the real line with this property.
E. Horozov
openaire +4 more sources
On extreme zeros of classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 2006 Let $x_1$ and $x_k$ be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree $k.$ We shall establish sharp inequalities of the form $x_1 B,$ which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical ...
Ilia Krasikov
openaire +4 more sources
On moments of classical orthogonal polynomials
Journal of Mathematical Analysis and Applications, 2015 Abstract In this work, using the inversion coefficients and some connection coefficients between some polynomial sets, we give explicit representations of the moments of all the orthogonal polynomials belonging to the Askey–Wilson scheme. Generating functions for some of these moments are also provided.
P. Njionou Sadjang +3 more
openaire +3 more sources
Zero distribution of sequences of classical orthogonal polynomials [PDF]
Abstract and Applied Analysis, 2003 We obtain the zero distribution of sequences of classical orthogonal polynomials associated with Jacobi, Laguerre, and Hermite weights. We show that the limit measure is the extremal measure associated with the corresponding weight.
Plamen Simeonov
doaj +2 more sources
Results on the associated classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 1995 AbstractLet {Pk(x)} be any system of the classical orthogonal polynomials, and let {Pk(x; c)} be the corresponding associated polynomials of order c (c ∈ N). Second-order recurrence relation (in k) is given for the connection coefficient an−1,k(c) in Pn−1(x;c)=σk=0n−1 an−1,k(c)Pk(x).
Stanisław Lewanowicz
openaire +3 more sources
On ( p , q ) $(p,q)$ -classical orthogonal polynomials and their characterization theorems
Advances in Difference Equations, 2017 In this paper, we introduce a general ( p , q ) $(p, q)$ -Sturm-Liouville difference equation whose solutions are ( p , q ) $(p, q)$ -analogues of classical orthogonal polynomials leading to Jacobi, Laguerre, and Hermite polynomials as ( p , q ) → ( 1 ...
M Masjed-Jamei +3 more
doaj +2 more sources
Classical orthogonal polynomials: dependence of parameters
Journal of Computational and Applied Mathematics, 2000 AbstractMost of the classical orthogonal polynomials (continuous, discrete and their q-analogues) can be considered as functions of several parameters ci. A systematic study of the variation, infinitesimal and finite, of these polynomials Pn(x,ci) with respect to the parameters ci is proposed.
A. Zarzo +3 more
openaire +4 more sources
Contemporary Mathematics, 2023 In this paper, new operational matrices (OMs) of ordinary and fractional derivatives (FDs) of a first finite class of classical orthogonal polynomials (FFCOP) are introduced.
H. M. Ahmed
semanticscholar +1 more source