Two points Pade type approximants for Stieltjes functions

Abstract

In this paper we study sequences of two point Padé type approximants for functions of the form

$$H\left( z \right) = \int_a^b {\frac{{d\phi \left( x \right)}}{{1 + zx}}}$$

through the interpolation of the generating function (1+zx)⁻¹ by Laurent polynomials. We give results on geometric and uniform convergence when the interpolatory knots are chosen i) as the zeros of certain orthogonal polynomials and ii) equally spaced on the interval (a,b). We show several applications to special functions.