Quadrature on the half-line and two-point Pade approximants to Stieltjes functions .2. Convergence

[摘要] Let alpha be a distribution function on [a, b] (0 less than or equal to a < b less than or equal to + infinity) such that the moment c(k) = integral(a)(b) x(k) d alpha(x) exist for all the integers k. The main course of the paper is to give convergence results both for sequences of two-point Pade approximants to the Cauchy transform of the distribution alpha (Stieltjes function) and for quadrature formulas based on exactly integrating Laurent polynomials. The case when d alpha(x) = k(x) dx, k(x) being a possibly complex function is also considered and estimates of the rate of convergence are given.

[发布日期] 1997-01-13

[效力级别]  Proceedings Paper

[关键词] two-point Pade approximation;Stieltjes function;orthogonal Laurent polynomials;quadrature formula