Authors: Tričković, Slobodan
Stanković, Miomir 
Title: On the orthogonality of classical orthogonal polynomials
Journal: Integral Transforms and Special Functions
Volume: 14
Issue: 2
First page: 129
Last page: 138
Issue Date: 1-Jan-2003
Rank: M23
ISSN: 1065-2469
DOI: 10.1080/10652460290029699a
Abstract: 
We consider the orthogonality of rational functions Wn(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 functions Wn(s). Thus we have shown that the orthogonality relations of the Jacobi and Laguerre polynomials are equivalent to the orthogonality of rational functions which are essentially the images of the classical orthogonal polynomials under the Laplace transform.
Keywords: Classical orthogonal polynomials | Laplace transform
Publisher: Taylor & Francis

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