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

Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w( x) on [0, 2π) 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...

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Bibliographic Details
Published in:Applied mathematics and computation 2008-05, Vol.198 (2), p.559-573
Main Authors: MILOVANOVIC, Gradimir V, CVETKOVIC, Aleksandar S, STANIC, Marija P
Format: Article
Language:English
Subjects:
Approximations and expansions
Exact sciences and technology
Fourier analysis
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Orthogonality
Recurrence relation
Sciences and techniques of general use
Special functions
Trigonometric polynomials of semi-integer degree
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Summary:Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w( x) on [0, 2π) 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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.08.062