Modified moments and Gaussian quadratures

Abstract

A number of the speakers at this conference have referred to or made use of the close connection between Pad approximants, continued fractions, moment theory, orthogonal polynomials, and (Gaussian) quadrature formulas. I want to discuss an application of a recent development in the theory (and practice) of Gaussian quadratures which may well have repercussions in other of these areas, namely, the modified moments procedure discussed recently by Sack and Donovan [ 14] and Gautschi [ 1].