Titlebook: Orthogonal Polynomials and their Applications; Proceedings of an In Manuel Alfaro,Jesús S. Dehesa,Jaime Vinuesa Conference proceedings 1988

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A review of orthogonal polynomials satisfying boundary value problems, The first three are classical, with well known properties, including weights, orthogonality, moments. The fourth is less well known. A real weight has not been found..All, however, are orthogonal with respect to a distributional weight . where μ. is the nth moment associated with the polynomials an

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Factorization of second order difference equations and its application to orthogonal polynomials, shift operator, can be factored as the product of two first order expressions. This result is used to obtain asymptotics over the complex plane for a class of polynomials orthonormal over the real line.

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The distribution of zeros of the polynomial eigenfunctions of ordinary differential operators of arlated via its moments directly in terms of the parameters which characterize the operators. Some results of K.M. Case and the authors are extended. In particular, the restriction for the degree of the polynomial coefficient of the ith-derivative to be not greater than i is relaxed. Applications to t

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Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials,vided difference operator used here is essentially the Askey-Wilson operator . where y.(x) and y.(x) are the two roots of Ay.+2Bxy+Cx.++2Dy+2Ex+f=0..The related Laguerre-Hahn orthogonal polynomials are then introduced as the denominators P.,P.,… of the successive approximants Q./P. of the Gauss-Hein

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978-3-540-19489-7Springer-Verlag Berlin Heidelberg 1988