Some extension of the Bessel-type orthogonal polynomials

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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 is an element of 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-n(alpha,M0,M1)(x). In particular, a hypergeometric representation (F-4(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-n(alpha,M0,M1)(x)/B-n(alpha)(x), outside of the closed contour Gamma containing the origin and the difference between the new polynomials and the classical ones, inside Gamma.
Publisher
GORDON BREACH SCI PUBL LTD
Issue Date
1998
Language
English
Article Type
Article
Keywords

SOBOLEV

Citation

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, v.7, no.3-4, pp.191 - 214

ISSN
1065-2469
URI
http://hdl.handle.net/10203/75746
Appears in Collection
MA-Journal Papers(저널논문)
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