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

作者：Duenas Herbert; Marcellan Francisco^*

来源：Journal of Computational and Applied Mathematics, 2010, 235(4): 998-1007.

DOI：10.1016/j.cam.2009.07.055

• Quasi-orthogonal polynomials
• Laguerre polynomials
• Soholev-type inner products
• Bessel function
• Relative asymptotics
• Outer relative asymptotics
• Mehler-Heine formula

In this paper we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-type inner product
< p, q >(s) =integral(infinity)(0) p(x)q(x)x(alpha)e(-x) dx + P(0)(t)AQ(0). alpha > -1,
where p and q are polynomials with real coefficients,
A = (M-0 lambda lambda M-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.

• 出版日期2010-12-15