Quadrature on the half-line and two-point Pade: Approximants to Stieltjes functions .1. Algebraic aspects

[摘要] Let f(z) be a Stieltjes function with asymptotic expansions L(0) and L(infinity) at z = O and z = infinity, respectively. Let [k/n] denote the two-point Padi approximant of type (m, n) which matches k of the coefficients of the series L(0) and which takes its remaining interpolation conditions from L(infinity). We discuss in this paper the algebraic aspects of this problem. We shall emphasize the relation between quadrature formulas and two-point Pade approximants and derive expressions for the error. Ln a subsequent paper we shall consider the convergence aspects of these approximants. For example, the positivity of the error, which is obtained here, will result in the monotonic convergence of certain sequences of two-point Pade approximants, a property which is well known in the case of classical Pade approximants.

[发布日期] 1995-12-29

[效力级别]  Proceedings Paper

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