Results 181 to 190 of about 351,291 (192)

On bivariate classical orthogonal polynomials

Applied Mathematics and Computation, 2018
Abstract We deduce new characterizations of bivariate classical orthogonal polynomials associated with a quasi-definite moment functional, and we revise old properties for these polynomials. More precisely, new characterizations of classical bivariate orthogonal polynomials satisfying a diagonal Pearson-type equation are proved: they are solutions of
Teresa E. Pérez, Miguel A. Piñar, Francisco Marcellán, Francisco Marcellán, Misael E. Marriaga   +4 more
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Classical Continuous Orthogonal Polynomials [PDF]

, 2020
Classical orthogonal polynomials (Hermite, Laguerre, Jacobi and Bessel) constitute the most important families of orthogonal polynomials. They appear in mathematical physics when Sturn-Liouville problems for hypergeometric differential equation are studied. These families of orthogonal polynomials have specific properties. Our main aim is to: 1.
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Classical Orthogonal Polynomials

1999
Example 7.2.5 discussed only one of the many types of the so-called classical orthogonal polynomials. Historically, these polynomials were discovered as solutions to differential equations arising in various physical problems. Such polynomials can be produced by starting with 1,x,x 2,… and employing the Gram-Schmidt process.
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Classical Orthogonal Polynomials as Moments

Canadian Journal of Mathematics, 1997
AbstractWe show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures.We use this fact to derive bilinear and multilinear generating functions for some of these polynomials.
Dennis Stanton, Mourad E. H. Ismail
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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 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
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The classical orthogonal polynomials

2016
Roderick Wong, Richard Beals
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Classical and Generalized Classical Orthogonal Polynomials

2001
Charles F. Dunkl, Yuan Xu
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Generalized Classical Orthogonal Polynomials

2014
Charles F. Dunkl, Yuan Xu
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Semi-classical orthogonal polynomials

1985
H. van Rossum, Erik Hendriksen
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