The Laguerre-Sobolev-type orthogonal polynomials

作者：Duenas Herbert; Marcellan Francisco^*

来源：Journal of Approximation Theory, 2010, 162(2): 421-440.

DOI：10.1016/j.jat.2009.07.006

• Quasi-orthogonal polynomials
• Laguerre polynomials
• Relative asymptotics
• Mehler-Heine formula
• Zeros

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 + N(p)((j))(0)(q)((j))(0),
where N is an element of R(+) and j is an element of N.
We Will focus Our attention on the outer relative asymptotics with respect to the standard Laguerre polynomials as well as oil all analog of the Mehler-Heine formula for the rescaled polynomials.

• 出版日期2010-2