A note on the error in gaussian quadrature

摘要

The error in Gaussian quadrature is analyzed using methods from the theory of analytic functions. It is well known that the error term may be expressed in terms of a contour integral against a kernel function Kn(t). We give two methods for computing the coefficients (in terms of the moments) for the Laurent series of Kn(t), and we give explicit expressions for Kn(t) for two particular measures. We then use the Laurent expansion of Kn(t) to estimate the error for various functions and measures.