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Variational calculus approach to Zernike polynomials with application to fluorescence correlation spectroscopy

Gligonov I, Enderlein J.
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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
F. Marcellán, M. Marriaga, T. Pérez, M. Piñar   +3 more
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The classical orthogonal polynomials

, 2016
R. Beals, R. Wong
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On classical orthogonal polynomials

Constructive Approximation, 1995
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Sergei K. Suslov, Natig M. Atakishiyev, Mizan Rahman   +2 more
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On the Orthogonality of Classical Orthogonal Polynomials

Integral Transforms and Special Functions, 2003
We consider the orthogonality of rational functions W n ( s ) as the Laplace transform images of a set of orthoexponential functions, obtained from the Jacobi polynomials, and as the Laplace transform images of the Laguerre polynomials. We prove that the orthogonality of the Jacobi and the Laguerre polynomials is induced by the orthogonality of the ...
Miomir S. Stanković, Slobodan B. Tričković   +1 more
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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.
Kil Hyun Kwon, B. H. Yoo, J. K. Lee
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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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2-Orthogonal polynomials and Darboux transformations. Applications to the discrete Hahn-classical case

, 2021
In this paper, we are interested in the following problem. We assume that is a monic 2-orthogonal polynomial sequence and we analyse the existence of a sequence of 2-orthogonal polynomials such that we have a decomposition This constitutes the ...
F. Marcellán, H. Chaggara, N. Ayadi
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