Difference Equation for Modifications of Meixner Polynomials
15 Aug 1995-Journal of Mathematical Analysis and Applications (Academic Press)-Vol. 194, Iss: 1, pp 250-258
TL;DR: In this paper, a modification of Meixner moment functional by adding a mass point at x = 0 was considered, and the resulting orthogonal polynomials, identified as hypergeometric 3F2 functions, were given the solution to a problem raised by R. Askey.
About: This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1995-08-15 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Meixner polynomials & Discrete orthogonal polynomials.
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TL;DR: In this paper, it was shown that the Laguerre-Hahn polynomials on arbitrary nonuniform lattice are covariant with respect to the Stieltjes function with polynomial coefficients.
205 citations
TL;DR: In this paper, the discrete semiclassical orthogonal polynomials of class s = 1 were studied and five canonical families were obtained by considering all possible solutions of the Pearson equation.
Abstract: 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.
26 citations
Cites background from "Difference Equation for Modificatio..."
...Perturbations of discrete semiclassical functionals by Dirac masses were studied in [2], [6], [24], [28], as well as in [3], [4], and [5]....
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TL;DR: In this article, a unified approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one perturbed by the addition of one or more Dirac deltafunctions is given.
Abstract: We give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explicitly, aswell as some asymptotic formulas. With special emphasis will be consideredthe second order differential equations that such polynomials satisfy. Theyallow us to obtain the central moments and the WKB approximation of thedistribution of zeros. Some examples coming from quadratic polynomialmappings and tridiagonal periodic matrices are also studied.
20 citations
TL;DR: In this paper, discrete semiclassical orthogonal polynomials of class s ≤ 2 were studied and the canonical families in each class were obtained by considering all possible solutions of the Pearson equation.
Abstract: In this contribution, discrete semiclassical orthogonal polynomials of class s ≤ 2 are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We also consider limit relations between these and other families of orthogonal polynomials.
19 citations
TL;DR: In this paper, a modification of moment functionals for some classical polynomials of a discrete variable by adding a mass point at x = O was considered, and the resulting orthogonal polynomorphisms were identified as hypergeometric functions and derived the second-order difference equation.
17 citations