Asymptotics for Laguerre-Sobolev type orthogonal polynomials modified within their oscillatory regime

作者：Huertas Edmundo J^*; Marcellan Francisco; Francisca Perez Valero M; Quintana Yamilet

来源：Applied Mathematics and Computation, 2014, 236: 260-272.

DOI：10.1016/j.amc.2014.03.038

• Orthogonal polynomials
• Discrete Sobolev polynomials
• Laguerre polynomials
• Asymptotics

In this paper we consider sequences of polynomials orthogonal with respect to the discrete Sobolev inner product %26lt;br%26gt;%26lt; f,g %26gt;(s) = integral(infinity)(0) f(x)g(x)x(alpha)e(-x)dx + F(c)AG(c)(i,) alpha %26gt;-1, %26lt;br%26gt;where f and g are polynomials with real coefficients, A is an element of R-(2,R-2) and the vectors F(c), G(c) are %26lt;br%26gt;A - ( M 0 0 N), F(c) -(f(c),f%26apos;(c)) and G(c) - (g(c),g%26apos;(c)), respectively, %26lt;br%26gt;with M; N is an element of R+ and the mass point c is located inside the oscillatory region for the classical Laguerre polynomials. We focus our attention on the representation of these polynomials in terms of classical Laguerre polynomials and we analyze the behavior of the coefficients of the corresponding five- term recurrence relation when the degree of the polynomials is large enough. Also, the outer relative asymptotics of the Laguerre- Sobolev type with respect to the Laguerre polynomials is analyzed.

• 出版日期2014-6-1