Results 211 to 220 of about 73,008 (249)

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
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Discrete (Legendre) orthogonal polynomials—a survey

International Journal for Numerical Methods in Engineering, 1974
AbstractThe discrete (Legendre) orthogonal polynomials, (DLOP's) are useful for approximation purposes. This set of mth degree polynomials {Pm(K, N)} are orthogonal with unity weight over a uniform discrete interval and are completely determined by the normalization Pm(O, N) = 1.
Neuman, C. P., Schonbach, D. I.
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On Generating Discrete Orthogonal Bivariate Polynomials

BIT Numerical Mathematics, 2002
This paper is concerned with an algorithm for recursively generating discrete orthogonal bivariate polynomials on a finite set \(S\left \{ (x_j,y_j) \right \} _{j=1}^n \in \mathbb R ^2 \) with respect to a weight vector \(m=(m_1,\dots ,m_n)\) having unit mass.
Huhtanen, Marko, Larsen, Rasmus Munk
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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.
Ronveaux, André, Salto, L.
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Stieltjes’ theorem for classical discrete orthogonal polynomials

Journal of Mathematical Physics, 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 orthogonal polynomials.
K. Castillo, F. R. Rafaeli, A. Suzuki
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Hermite Orthogonal Polynomials of a Discrete Variable

Journal of Computational Methods in Sciences and Engineering, 2002
The Hermite orthogonal polynomials on a discrete point set are constructed. A discrete point set, a weight function and normalizing factors are obtained, and the orthogonality of them is proved. The problems of an approximation of functions by one, two and three variables with the help of interpolation of the Hermite series constructed on the ...
Streltsova, O. I., Streltsov, I. P.
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Discrete orthogonal matrix polynomials

Analysis Mathematica, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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. Guemo Tefo, Iván Area, M. Foupouagnigni   +2 more
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Chopped Orthogonal Polynomial Expansions—Some Discrete Cases

SIAM Journal on Algebraic Discrete Methods, 1983
We study expansions of functions $f ( x )$ in terms of certain discrete families of orthogonal polynomials, $\{ p_i ( x ) \}$ where $x = 0,1, \cdots ,N,N$ finite or infinite. We assume f is known for $x\leqq M( M < N )$ and that the expansion in terms of the $p_i $’s is chopped after L terms $( L < N )$.
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Difference Equations and Discriminants for Discrete Orthogonal Polynomials

The Ramanujan Journal, 2005
Let \(\{p_n(x)\}\) be a sequence of discrete orthogonal polynomials satisfy orthogonality relation \[ \sum_{l=s}^t p_m(l)p_n(l)w(l)=\kappa_m \delta_{m,n} \qquad \qquad \sum_{l=s}^t w(l)=1 \] where \(w\) is a weight function. \(l \in \{s, s+1, \dots, t\} \subset \mathbf{R}\), \(s\) is finite but \(t\) is finite or infinite.
Ismail, Mourad E. H., Nikolova, Inna, Simeonov, Plamen   +2 more
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