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Orthogonal polynomials with respect to the Laguerre measure perturbed by the canonical transformations. (English) Zbl 1215.33007

The Laguerre measure \(d \mu\) supported on \([0, \infty)\) is perturbed by the three canonical transformations: the Christoffel transformation (\(d \hat{\mu}=(. - \xi) d \mu\), \(\xi \notin [0,\infty\))), the Uvarov transformation (\(d \hat{\mu}= d \mu+ M \delta_{\xi}\), \(\xi \notin [0,\infty)\) and \(M>0\)) and the Geronimus transformation (\(d \hat{\mu}=\frac{ d \mu}{.-\xi}+ M \delta_{\xi}\), \(\xi \notin [0,\infty)\) and \(M>0\)).
The authors analyse properties of the orthogonal polynomials with respect to the perturbed measures and they obtain the second-order linear differential equation satisfied by these polynomials. Finally, they also obtain several asymptotic properties for these polynomials.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C47 Other special orthogonal polynomials and functions

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