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Some extension of the Bessel-type orthogonal polynomials

 

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Opened Access Some extension of the Bessel-type orthogonal polynomials
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Author: Arvesú Carballo, Jorge
Álvarez Nodarse, Renato
Marcellán Español, Francisco
Kwon, Kil Hyun
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 1998
Published in: Integral Transforms and Special Functions, 7 (3-4), 191-214.
Document type: Article
Abstract: We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional M0 (x) + M1 0 (x), where M0 and M1 2 IR. We give necessary and su cient conditions in order for this functional to be a quasi-de nite functional. In such a situation we analyze the corresponding sequence of monic orthogonal polynomials B ;M0;M1 n (x). In particular, a hypergeometric representation (4F2) for them is obtained. Furthermore, we deduce a relation between the corresponding Jacobi matrices, as well as the asymptotic behavior of the ratio B ;M0 ;M1 n (x)=B n (x), outside of the closed contour containing the origin and the di erence between the new polynomials and the classical ones, inside.
Cite: Arvesú Carballo, J., Álvarez Nodarse, R., Marcellán Español, F. y Kwon, K.H. (1998). Some extension of the Bessel type orthogonal polynomials. Integral Transforms and Special Functions, 7 (3-4), 191-214.
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URI: http://hdl.handle.net/11441/41730

DOI: 10.1080/10652469808819199

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