Citation:
Integral Transforms and Special Functions, 1998, vol. 7, n. 3-4, p. 191-214

ISSN:
1065-2469

DOI:
10.1080/10652469808819199

Sponsor:
The work of the first three authors was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB 96-0120-C03-01. The fourth author (KHK) thanks KOSEF(95-070-02-01-3) and Korea Ministry of Education (BSR1 1420) for their research support.

We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional $M_0\delta(x)+M_1\delta'(x)$, where $M_0$ and $M_1\in\bf R$. We give necessary and sufficient conditions in order for this functional to be a quasi-We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional $M_0\delta(x)+M_1\delta'(x)$, where $M_0$ and $M_1\in\bf R$. We give necessary and sufficient conditions in order for this functional to be a quasi-definite functional. In such a situation we analyze the corresponding sequence of monic orthogonal polynomials $B^{\alpha,M_0,M_1}_n(x)$. In particular, a hypergeometric representation $(_4F_2)$ for them is obtained.[+][-]

Furthermore, we deduce a relation between the corresponding Jacobi matrices, as well as the asymptotic behavior of the ratio $B^{\alpha,M_0,M_1}_n(x)/B^\alpha_n(x)$, outside the closed contour $\Gamma$ containing the origin, and the difference between the new Furthermore, we deduce a relation between the corresponding Jacobi matrices, as well as the asymptotic behavior of the ratio $B^{\alpha,M_0,M_1}_n(x)/B^\alpha_n(x)$, outside the closed contour $\Gamma$ containing the origin, and the difference between the new polynomials and the classical ones, inside $\Gamma$.[+][-]

Description:

24 pages, no figures.-- MSC1991 codes: 33C45, 33A65, 42C05.