Asymptotic behaviour of Laguerre-Sobolev-type orthogonal polynomials. A nondiagonal case

Authors:
Herbert Dueñas;Francisco Marcellán
Affiliations:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain and Universidad Nacional de Colombia, Departamento de Matemáticas, ...;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 3
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Abstract

In this paper we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-type inner product "S=@!"0^~p(x)q(x)x^@ae^-^xdx+P(0)^tAQ(0),@a-1, where p and q are polynomials with real coefficients, A=(M"0@l@lM"1),P(0)=(p(0)p^'(0)),Q(0)=(q(0)q^'(0)), and A is a positive semidefinite matrix. We will focus our attention on their outer relative asymptotics with respect to the standard Laguerre polynomials as well as on an analog of the Mehler-Heine formula for the rescaled polynomials.