Error bound of certain Gaussian quadrature rules for trigonometric polynomials

Marija P. Stanić, Aleksandar S. Cvetković, Tatjana V. Tomović

In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function $w(x)=1+\cos x$, $x\in(-i,i)$, for $2i$-periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.