Gaussian quadrature rules and numerical examples for strong extensions of mass distribution functions

The theory of strong moment problems has provided Gaussian quadrature rules for approximate integration with respect to strong distributions. In Hagler (Ph.D. Thesis, University of Colorado, Boulder, 1997) and Hagler et al. (Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, in press), a transformation of the form v(x)=(1/λ)(x−γ/x), λ,γ>0, is used to obtain strong mass distribution functions from mass distribution functions. This transformation also links the systems of orthogonal polynomials and Laurent polynomials and their zeros. In this paper we show how the transformation method can be used to obtain the Gaussian quadrature rules for strong extensions of mass distribution functions. We then provide numerical examples of strong Gaussian quadrature approximations to the integrals of elementary functions with respect to selected strong distributions.