Bounds of the error of Gauss-Turan-type quadratures, II

摘要

This paper is concerned with bounds on the remainder term of the Gauss-Turan quadrature formula,rnR_(n,s)(f)=1∫(-1)f(t)w(t)dt-n∑(v=1) 2s∑(i=0)λ_(i,v)f~((i))(τ_v),rnwherernw(t)=w_(n,e)(t)=[U_(n-1)(t)]~(2e)(1-t~2)~(e-1/2)(e∈N),rnU_(n-1), denotes the (n - 1)th degree Chebyshev polynomial of the second kind and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at ±1 and the sum of semi-axes q > 1.