Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type
All coherent pairs for Sobolev orthogonal polynomials were obtained in 1997 by \textit{H. G. Meijer} [J. Approximation Theory 89, No. 3, 321-343 (1997; Zbl 0880.42012)]. For Laguerre coherent pairs \((\psi_0,\psi_1)\) one of the measure has to be a Laguerre weight and the other is a modification of a Laguerre weight by a rational function and/or a Dirac measure. The asymptotics of the Sobolev orthogonal polynomials is worked out for both cases, using the well-known asymptotics of Laguerre polynomials (in particular Perron's formula in the complex plane).
scientific article; zbMATH DE number 1471629