Error Estimates for Interpolatory Quadrature Formulae.
In this note quadrature formula with error estimate for functions with simple pole is discussed. Chebyshev points of the second kind are used as the nodes of integration.
Let be a hyperplane and let be given. Denote In this paper the problem of calculating of the constant is studied. We present a complete characterization of those for which . Next we consider the case . Finally some computer examples will be presented.
We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.