Asymptotic properties of Laguerre-Sobolev type orthogonal polynomials

被引：11
作者：
Duenas, Herbert [2 ]
Huertas, Edmundo J. [1 ]
Marcellan, Francisco [1 ]
机构：
[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
[2] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia
来源：
NUMERICAL ALGORITHMS | 2012年 / 60卷 / 01期
关键词：
Orthogonal polynomials; Laguerre polynomials; Laguerre-Sobolev-type orthogonal polynomials; Bessel functions; Rescaled polynomials; Asymptotics; Plancherel-Rotach type formula; Outer relative asymptotics; Mehler-Heine type formula; MONOTONICITY; ZEROS;
D O I：
10.1007/s11075-011-9511-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this contribution we consider the asymptotic behavior of sequences of monic polynomials orthogonal with respect to a Sobolev-type inner product < p, q >(S) = integral(infinity)(0) 1p(x)q(x)x(alpha)e(-x)dx + Np'(a)q' (a), alpha < -1 where N is an element of R+ , and a is an element of R-. We study the outer relative asymptotics of these polynomials with respect to the standard Laguerre polynomials. The analogue of the Mehler-Heine formula as well as a Plancherel-Rotach formula for the rescaled polynomials are given. The behavior of their zeros is also analyzed in terms of their dependence on N.
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页码：51 / 73
页数：23
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