A generalization of Laguerre polynomials
SIAM Journal on Mathematical Analysis
Sobolev-type orthogonal polynomials: the nondiagonal case
Journal of Approximation Theory
Quasi-orthogonality with applications to some families of classical orthogonal polynomials
Applied Numerical Mathematics
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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.