Monotony in interpolatory quadratures

Summary Let, be holomorphic in an open disc with the centrez₀=0 and radiusr>1. LetQ_n (n=1, 2, ...) be interpolatory quadrature formulas approximating the integral. In this paper some classes of interpolatory quadratures are considered, which are based on the zeros of orthogonal polynomials corresponding to an even weight function. It is shown that the sequencesQ_n9f] (n=1, 2, ...) are monotone. Especially we will prove monotony in Filippi's quadrature rule and with an additional assumption onf monotony in the Clenshaw-Curtis quadrature rule.