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Abstract: We derive the fourth order difference equation satisfied by the associated of order r of the classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials oe and which appear in the discrete Pearson equation \Delta(oe ae) = ae defining the weight ae(x) of the classical discrete orthogonal polynomials. (Update)
Context of citations to this paper: More
.... equation for the associated polynomials of all classical discrete polynomials were given for all integers r (order of association) in [5], using the properties of the Stieltjes functions of the associated linear forms. On the other hand, the equation for the first associated (r...
...to the derivation of these fourth order difference equations. Their polynomial coefficients have been given explicitly in Refs. [1,7,8,10,19,32,36] for the rth associated classical discrete orthogonal polynomials. In 1999, using symmetry properties inside the three term...
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BibTeX entry: (Update)
M.Foupouagnigni, A. W. Koepf, A. Ronveaux, The fourth-order difference equation for the associated classical discrete orthogonal polynomials. Letter, J. Comput. Appl. Math. (in print). http://citeseer.ist.psu.edu/571359.html More
@misc{ foupouagnigni-fourthorder,
author = "M. Foupouagnigni and A. Koepf and A. Ronveaux",
title = "The fourth-order difference equation for the associated classical discrete
orthogonal polynomials",
text = "M.Foupouagnigni, A. W. Koepf, A. Ronveaux, The fourth-order difference
equation for the associated classical discrete orthogonal polynomials. Letter,
J. Comput. Appl. Math. (in print).",
url = "citeseer.ist.psu.edu/571359.html" }
Citations (may not include all citations):59 Classical Orthogonal Polynomials of a Discrete Variable (context) - Nikiforov, Suslov et al. - 1991
8 Fourth-order differential equation satisfied by the associat.. (context) - Zarzo, Ronveaux et al. - 1993
8 Fourth-order differential equation satisfied by the associat.. (context) - Belmehdi, Ronveaux - 1991
8 Results on the associated classical orthogonal polynomials (context) - Lewanowicz - 1995
7 The fourth-order difference equation satisfied by the associ.. - Foupouagnigni, Ronveaux et al. - 1997
7 Algorithms for classical orthogonal polynomials - Koepf, Schmersau - 1996
6 Difference equation for the associated polynomials on the li.. (context) - Atakishiyev, Ronveaux et al. - 1996
6 Uber Polynomlosungen von Differentialgleichungen und Differe.. (context) - Lesky - 1985
4 Fourth order difference equation for the associated Meixner .. - Letessier, Ronveaux et al. - 1996
4 Fourth order difference equation for the first associated of.. (context) - Ronveaux, Godoy et al.
3 th order differential equation and orthogonal polynomials of.. (context) - Ronveaux - 1991
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