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

Gligonov I, Enderlein J.
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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.
Kwon, K. H., Lee, J. K., Yoo, B. H.
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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 ...
Slobodan TriČkoviĆ, Miomir StankoviĆ
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On classical orthogonal polynomials

Constructive Approximation, 1995
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Atakishiyev, N. M., Rahman, M., Suslov, S. K.   +2 more
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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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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.
George E. Andrews, Richard Askey
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Classical Orthogonal Polynomials

1991
Classical orthogonal Polynomials — the Jacobi, Laguerre and Hermite polynomials — form the simplest class of special functions. At the same time, the theory of these polynomials admits wide generalizations. By using the Rodrigues formula for the Jacobi, Laguerre and Hermite polynomials we can come to integral representations for other special functions
Arnold F. Nikiforov, Vasilii B. Uvarov, Sergei K. Suslov   +2 more
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