Abstract
Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31-55, (English translation in East J. Approx. 11 (2005) 337-359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi-integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, Berlin, 1970], and Dryanov [Numer. Math. 67 (1994), 441-464], considered quadrature rules of interpolatory type with multiple nodes with maximal trigonometric degree of exactness. Inspired by their results, we study here s-orthogonal trigonometric polynomials of semi-integer degree. In particular, we consider the case of an even weight function.
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