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

This paper is concerned with bounds on the remainder term of the Gauss-Turán quadrature formula,Rn,s(f)=∫−11f(t)w(t)dt−∑ν=1n∑i=02sλi,νf(i)(τν), wherew(t)=wn,ℓ(t)=[Un−1(t)/n]2ℓ(1−t2)ℓ−1/2(ℓ∈N), Un−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 ϱ>1.