Explicit formulas for five-term recurrence coefficients of orthogonal trigonometric polynomials of semi-integer degree

被引：14

作者：

Milovanovic, Gradimir V. ^{[1
]}

Cvetkovic, Aleksandar S. ^{[1
]}

Stanic, Marija P. ^{[2
]}

机构：

[1] Univ Nis, Fac Elect Engn, Dept Math, Nish 18000, Serbia

[2] Univ Kragujevac, Fac Sci, Dept Math & Informat, Kragujevac 34000, Serbia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 198卷 / 02期

关键词：

trigonometric polynomials of semi-integer degree; orthogonality; recurrence relation;

D O I：

10.1016/j.amc.2007.08.062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x) on [0,2 pi) have been considered firstly by Turetzkii in [ A. H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337 - 359 (Translation in English from Uchenye Zapiski, Vypusk 1(149), Seria math. Theory of Functions, Collection of Papers, Izdatel'stvo Belgosuniversiteta imeni V. I. Lenina, Minsk (1959) 31 - 54)]. It is proved that such orthogonal trigonometric polynomials of semi-integer degree satisfy five-term recurrence relation. In this paper we present explicit formulas for five-term recurrence coefficients for some weight functions. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：559 / 573

页数：15