Orthogonal rational functions and quadrature on the real half line

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Pade´ approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Pade´ approximants is discussed. [Copyright &y& Elsevier]