Integral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions

Abstract

We evaluate explicitly the integrals , with the being any one of the four Chebyshev polynomials of degree . These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature formulae with Chebyshev abscissae, when the function to be integrated is analytic in a domain containing in its interior.