Results 291 to 300 of about 411,141 (342)

The classical orthogonal polynomials

2016
Roderick Wong, Richard Beals
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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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On classical orthogonal polynomials

Constructive Approximation, 1995
Following the works of Nikiforov and Uvarov a review of the hypergeometric-type difference equation for a functiony(x(s)) on a nonuniform latticex(s) is given. It is shown that the difference-derivatives ofy(x(s)) also satisfy similar equations, if and only ifx(s) is a linear,q-linear, quadratic, or aq-quadratic lattice.
Sergei K. Suslov, Natig M. Atakishiyev, Mizan Rahman   +2 more
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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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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.
Richard Askey, George E. Andrews
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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
semanticscholar   +1 more source

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
Sergei K. Suslov, Arnold F. Nikiforov, Vasilii B. Uvarov   +2 more
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The Classical Orthogonal Polynomials

1988
In §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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Characterizations of Classical Orthogonal Polynomials

Results in Mathematics, 1993
We give a simple unified proof and an extension of some of the characterization theorems of classical orthogonal polynomials of Jacobi, Bessel, Laguerre, and Hermite. In particular, we prove that the only orthogonal polynomials whose derivatives form a weak orthogonal polynomial set are the classical orthogonal polynomials.
Kil Hyun Kwon, B. H. Yoo, J. K. Lee
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Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation

Studies in applied mathematics (Cambridge)
This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials.
A. Branquinho, Juan E. F. D'iaz, Ana Foulqui'e-Moreno, Manuel Mañas   +3 more
semanticscholar   +1 more source