The error norm of nonsymmetric product integration rules for Chebyshev weight functions with Chebyshev abscissae

Abstract We consider four product integration rules, two for the Chebyshev weight of the first-kind based on the Chebyshev abscissae of the third or fourth-kind, and another two for the Chebyshev weight of the second-kind based again on the Chebyshev abscissae of the third or fourth-kind. The new rules have positive weights given by explicit formulae, while the rules for the Chebyshev weight of the second-kind have the best possible degree of exactness for an interpolatory formula not of Gauss type. On certain spaces of analytic functions the error term of these rules is a continuous linear functional. By means of a new approach, we compute explicitly the norm of the error functional, which leads to efficient error bounds.