Some extension of the Bessel-type orthogonal polynomials

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 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.