Laguerre-Sobolev orthogonal polynomials: asymptotics for coherent pairs of type II

Authors:
Manuel Alfaro;Juan J. Moreno-Balcázar;M. Luisa Rezola
Affiliations:
Departamento de Matemáticas, Universidad de Zaragoza, Zaragoza 50009, Spain;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Spain;Departamento de Matemáticas, Universidad de Zaragoza, Zaragoza 50009, Spain
Venue:
Journal of Approximation Theory
Year:
2003

Citing 8
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Abstract

Let S n be polynomials orthogonal with respect to the inner product ( f,g ) S = ∫ 0 ∞ fg dµ 0 + λ ∫ 0 ∞ f'g' dµ 1 where dµ 0 = x α e -x dx, dµ 1 = x α+1 e -x /x-ξ dx + Mδξ with α - 1, ξ ≤ 0, M ≥0, and λ 0. A strong asymptotic on (0, ∞), a Mehler-Heine type formula, a Plancherel-Rotach type exterior asymptotic as well as an upper estimate for S n are obtained. As a consequence, we give asymptotic results for the zeros and critical points of S n and the distribution of contracted zeros. Some numerical examples are shown.