Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems

For analytic functions the remainder term of quadrature rules can be repres ented as a contour integral with a complex kernel function. From this repre sentation different remainder term estimates involving the kernel are obtai ned. It is studied in detail how polynomial biorthogonal systems can be app lied to derive sharp bounds for the kernel function. It is shown that these bounds are practical to use and can easily be computed. Finally, various n umerical examples are presented.