On certain symmetric strong distributions, two-point Padé approximation and related quadratures

Let ϕ be a c-inversive strong distribution as defined in [A. Sri Ranga, E.X.L. de Andrade, J.H. McCabe, Some consequences of a symmetry in strong distributions, J. Math. Anal. Appl. 193 (1) (1995) 158–168]. In this paper, two-point Padé approximants, both with free and prescribed poles, related to the distribution ϕ are analyzed. In particular, the existence of c-inversive rational approximants to the Stieltjes transform of ϕ is studied, in order to make computations in an advantageous way. An application to numerical quadratures is also given, and several examples applying these Gauss-type quadrature formulas in the case of integrands which can be well approximated by Laurent polynomials are displayed, showing better results than the corresponding for the usual Gaussian rules.