Results 1 to 10 of about 324,599 (288)
On discrete orthogonal polynomials of several variables [PDF]
Advances in Applied Mathematics, 2004 Let $V$ be a set of isolated points in $\RR^d$. Define a linear functional $\CL$ on the space of real polynomials restricted on $V$, $\CL f = \sum_{x \in V} f(x)\rho(x)$, where $\rho$ is a nonzero function on $V$.
Yuan Xu
core +6 more sources
Some discrete multiple orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2003 27 pages, no figures.-- MSC2000 codes: 33C45, 33C10, 42C05, 41A28.-- Issue title: "Proceedings of the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications" (OPSFA-VI, Rome, Italy, 18-22 June 2001).MR#: MR1985676
J. Arvesú +2 more
core +8 more sources
Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials [PDF]
Difference Equations, Special Functions and Orthogonal Polynomials
(Eds. S. Elaydi et al.), World Scientific, 2007, pp. 687-725, 2005 We give four examples of families of orthogonal polynomials for which the coefficients in the recurrence relation satisfy a discrete Painlev\'e equation. The first example deals with Freud weights $|x|^\rho \exp(-|x|^m)$ on the real line, and we repeat Freud's derivation and analysis for the cases $m=2,4,6$.
Walter Van Assche
arxiv +7 more sources
Laguerre–Freud Equations for the Gauss Hypergeometric Discrete Orthogonal Polynomials
Mathematics, 2023 The Cholesky factorization of the moment matrix is considered for the Gauss hypergeometric discrete orthogonal polynomials. This family of discrete orthogonal polynomials has a weight with first moment given by ρ0=2F1a,bc+1;η.
Itsaso Fernández-Irisarri +1 more
doaj +2 more sources
Pearson equations for discrete orthogonal polynomials: III—Christoffel and Geronimus transformations [PDF]
RACSAM, 2022 Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations.
Manuel Mañas
openalex +3 more sources
A General Method for Generating Discrete Orthogonal Matrices [PDF]
IEEE Access, 2021 Discrete orthogonal matrices have applications in information coding and cryptography. It is often challenging to generate discrete orthogonal matrices.
Ka-Hou Chan, Wei Ke, Sio-Kei Im
doaj +2 more sources
On zeros of discrete orthogonal polynomials [PDF]
Journal of Approximation Theory, 2009 This article is available open access through the publisher’s website at the link below. Copyright @ 2008 Elsevier Inc.We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials ...
Alexander Zarkh +15 more
core +5 more sources
Discrete transforms and orthogonal polynomials of (anti)symmetric multivariate cosine functions [PDF]
SIAM J. Numer. Anal. 52-6 (2014), pp. 3021-3055, 2014 The discrete cosine transforms of types V--VIII are generalized to the antisymmetric and symmetric multivariate discrete cosine transforms. Four families of discretely and continuously orthogonal Chebyshev-like polynomials corresponding to the antisymmetric and symmetric generalizations of cosine functions are introduced.
Hrivnák, Jiří, Motlochová, Lenka
arxiv +3 more sources
Multiplicity of zeros and discrete orthogonal polynomials [PDF]
Results in Mathematics, 2002 We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions $\sum a_i F_i(x)$, at a certain point $c,$ depending on the chosen family $\{F_i \}$. The most important example is a polynomial with $c=1.$ It is shown that this question naturally leads to discrete orthogonal polynomials.
Ilia Krasikov
openalex +5 more sources
Discrete semiclassical orthogonal polynomials of class one [PDF]
Pacific J. Math. 268 (2014) 389-411, 2012 We study the discrete semiclassical orthogonal polynomials of class s=1. By considering all possible solutions of the Pearson equation, we obtain five canonical families. We also consider limit relations between these and other families of orthogonal polynomials.
Francisco Marcellán, Diego Dominici
arxiv +8 more sources