Abstract

We examine the error in the optimal estimation of∫−11f(t)w(t)dt by a quadrature formula using values off at equally spaced points of (−1, 1) or at the zeros of ultraspherical polynomials. Heref is known to be an analytic function in the unit disc which is bounded by l andw is a given weight function with prescribed behavior near ±1. A major role in our investigations is played by bounds on (−1, 1) from above and below for the finite Blaschke product which is based in the nodes of the quadrature formula. Optimal estimation of the functionf, rather than its integral, is also studied.

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