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On classical orthogonal polynomials
Constructive Approximation, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergei K. Suslov +2 more
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On the Orthogonality of Classical Orthogonal Polynomials
Integral Transforms and Special Functions, 2003We 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 +1 more
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Characterizations of Classical Orthogonal Polynomials
Results in Mathematics, 1993In 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, 1997AbstractWe 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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Classical orthogonal polynomials
1985There 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.
Richard Askey, George E. Andrews
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Classical Orthogonal Polynomials
1991Classical 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
Sergei K. Suslov +2 more
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The Classical Orthogonal Polynomials
1988In §2 we introduced the polynomials y n (z) of hypergeometric type, which are solutions of $$\sigma \left( z \right)y'' + \tau \left( z \right)y' + \lambda y = 0$$ (1) with \(\lambda = {\lambda _n} = - n\tau ' - \frac{1}{2}n\left( {n - 1} \right)\sigma ''\)
Arnold F. Nikiforov, Vasilii B. Uvarov
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The H q -Classical Orthogonal Polynomials
Acta Applicandae Mathematica, 2002The 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.
L. Khériji, P. Maroni
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The Dω—classical orthogonal polynomials [PDF]
Results in Mathematics, 1997 This is an expository paper; it aims to give an essentially self-contained overview of discrete classical polynomials from their characterizations by Hahn’s property and a Rodrigues’ formula which allows us to construct it. The integral representations of corresponding forms are given.
P. Maroni, F. Abdelkarim
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