Orthogonal polynomials and second-order pseudo-spectral linear differential equations

被引：2

作者：

Marcellan, Francisco ^{[1
]}

Sfaxi, Ridha ^{[2
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[2] Fac Sci Gabes, Dept Math, Gabes 6072, Tunisia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2010年 / 21卷 / 07期

关键词：

orthogonal polynomials; three-term recurrence relations; semiclassical polynomials; first structure relations; second-order linear differential equations;

D O I：

10.1080/10652460903403240

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with monic orthogonal polynomial sequences which satisfy the second-order pseudo-spectral linear differential equation: phi(2)((x)y ''(x) + phi(1)(x)y'x) = chi(x, n)y(x), n is an element of N, where phi(i), i = 1, 2 are polynomials with phi(2) monic, and the degrees of the polynomials chi(., n) are uniformly bounded. These polynomial sequences are semiclassical of class either s = 0 or 1. They are, up to a linear change of variable, the classical polynomials (Hermite, Laguerre, Bessel, and Jacobi) and symmetric semiclassical polynomials of class one. For them, we deduce the three-term recurrence relations, the structure relations, and the second-order linear differential equations that these polynomial sequences satisfy.

引用

页码：487 / 501

页数：15