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Discrete Semiclassical Orthogonal Polynomials of Class 2 [PDF]

Pacific Journal of Mathematics, 2019
In this contribution, discrete semiclassical orthogonal polynomials of class $s\leq2$ are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class.
Diego Dominici, Francisco Marcell'an Espanol   +1 more
semanticscholar   +7 more sources

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Exceptional Orthogonal Polynomials via Krall Discrete Polynomials

, 2020
We consider two important extensions of the classical and classical discrete orthogonal polynomials: namely, Krall and exceptional polynomials. We also explore the relationship between both extensions and how they can be used to expand the Askey tableau.
A. J. Durán
semanticscholar   +3 more sources

Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions

International Journal of Systems Science, 2022
This paper investigates model order reduction (MOR) methods of discrete-time systems via discrete orthogonal polynomials in the time domain. First, this system is expanded under discrete orthogonal polynomials, and the expansion coefficients are computed
Zhaoxi Wang, Yaolin Jiang, Kangli Xu
semanticscholar   +1 more source

Bivariate Symmetric Discrete Orthogonal Polynomials

, 2017
In this paper, we analyze second-order linear partial difference equations having bivariate symmetric orthogonal polynomial solutions. We present conditions to have admissible, potentially self-adjoint partial difference equations of hypergeometric type having orthogonal polynomial solutions.
Y. G. Tefo, I. Area, M. Foupouagnigni
semanticscholar   +3 more sources

Stieltjes’ theorem for classical discrete orthogonal polynomials

, 2020
The purpose of this note is to establish, from the hypergeometric-type difference equation introduced by Nikiforov and Uvarov, new tractable sufficient conditions for the monotonicity with respect to a real parameter of zeros of classical discrete ...
K. Castillo, F. R. Rafaeli, A. Suzuki
semanticscholar   +1 more source

2-Orthogonal polynomials and Darboux transformations. Applications to the discrete Hahn-classical case

, 2021
In this paper, we are interested in the following problem. We assume that is a monic 2-orthogonal polynomial sequence and we analyse the existence of a sequence of 2-orthogonal polynomials such that we have a decomposition This constitutes the ...
F. Marcellán, H. Chaggara, N. Ayadi
semanticscholar   +1 more source

Discrete classical orthogonal polynomials

Journal of Difference Equations and Applications, 1998
We find necessary and sufficient conditions for the difference equation of hypergeometric type to have polynomial solutions , which are orthogonal, that is Traditionallydμ(x) is a positive measure but here we allow it to be a signed measure. We then show that the usual restrictions on parameters in discrete classical orthogonal polynomials can be ...
Kwon, KH Kwon, Kil Hyun, Lee, DW, Park, SB, Yoo, BH   +3 more
openaire   +2 more sources

Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame

, 2020
In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference
Bao Wang, Xiang-Ke Chang, Xing-Biao Hu, Shi-Hao Li   +3 more
semanticscholar   +1 more source

Discrete orthogonal polynomials – polynomial modification of a classical functional

Journal of Difference Equations and Applications, 2001
Polynomial modifications of a classical discrete linear functional are examined in detail, in particular when the new linear functional remains classical. New addition formulas are deduced for Charlier, Meixner and Hahn polynomials from the Christoffei representation and results are also given for a particular generalized Meixner family.
L. Salto, André Ronveaux
openaire   +3 more sources