Abstract. In 1985, Gautschi and the author constructed Gaussian quadrature formulae on (0, +∞) involving Einstein and Fermi functions as weights and applied then to the summation of slowly convergent series which can be represented in terms of the derivative of a Laplace transform, or in terms of the Laplace transform itself. A problem that may arise in this procedure is the determination of the respective inverse Laplace transform. For the class of slowly convergent series and R(s) is a rational function, Gautschi recently solved this problem. In the present paper, using complex integration and constructing Gauss-Christoffel quadratures on (0, +∞) with respect to the weight functions w 1 (t) = 1/ cosh 2 t and w 2 (t) = sinh t/ cosh 2 t, we reduce the and w 2 , respectively. We illustrate this method with a few numerical examples
