ON THE ORTHOGONALITY OF CLASSICAL ORTHOGONAL POLYNOMIALS

Authors: TRI Ccaron KOVIC´ S.¹; STANKOVIC´ M.²

Source: Integral Transforms and Special Functions, Volume 14, Number 3, June 2003 , pp. 271-280(10)

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Abstract:

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 functions W_n(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: Laplace transform; Classical orthogonal polynomials

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10652460290029699

Affiliations: 1: Department of Mathematics, Faculty of Civil Engineering, University of Ni scaron , Beogradska 14, 18000 Ni scaron , Serbia , Beogradska 14, 18000 Ni scaron , Serbia "> 2: Department of Mathematics, Faculty of Environmental Engineering, University of Ni scaron , Ccaron arnojevic´a 10a, 18000 Ni scaron , Serbia, Ccaron arnojevic´a 10a, 18000 Ni scaron , Serbia">