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Classical orthogonal polynomials

, 1985
There have been a number of definitions of the classical orthogonal polynomials, but each definition has left out some important orthogonal polynomials which have enough nice properties to justify including them in the category of classical orthogonal polynomials.
G. Andrews, R. Askey
semanticscholar   +2 more sources

On bivariate classical orthogonal polynomials

Applied Mathematics and Computation, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Marcellán   +3 more
semanticscholar   +3 more sources

Characterizations of Classical Orthogonal Polynomials

Results in Mathematics, 1993
In the literature several characterization theorems for the so-called classical orthogonal polynomials are known [cf. \textit{S. Bochner}, Math. Z. 29, 730-736 (1929), \textit{W. Hahn}, Math. Z. 39, 634-638 (1935), \textit{W. A. Al-Salam}, Orthogonal polynomials: theory and practice, Proc. NATO ASI, Colombus/OH (USA) 1989, NATO ASI Ser., Ser.
Kwon, K. H., Lee, J. K., Yoo, B. H.
openaire   +2 more sources

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.
Ismail, Mourad E. H., Stanton, Dennis
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The H q -Classical Orthogonal Polynomials

Acta Applicandae Mathematica, 2002
The authors expose the readers to a certain class of \(q\)-analogues of classical orthogonal polynomials such as \(q\)-Laguerre, little \(q\)-Laguerre, big \(q\)-Jacobi polynomials, etc. by presenting the results for this class of polynomials, most of them well-known in the literature, in a coherent form.
Khériji, L., Maroni, P.
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On classical orthogonal polynomials

Constructive Approximation, 1995
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Atakishiyev, N. M.   +2 more
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