Publication: Some extension of the Bessel-type orthogonal polynomials
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1998-10
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Taylor & Francis
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Abstract
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 polynomials and the classical ones, inside $\Gamma$.
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.
MR#: MR1775827 (2001b:33013)
Zbl#: Zbl 0936.33003
MR#: MR1775827 (2001b:33013)
Zbl#: Zbl 0936.33003
Keywords
Bessel polynomials, Semi-classical orthogonal polynomials, Hypergeometric functions, Second order differential equation, Three-term recurrence equation, Quasi-orthogonal polynomials, Perturbed orthogonal polynomials
Bibliographic citation
Integral Transforms and Special Functions, 1998, vol. 7, n. 3-4, p. 191-214