ABSTRACT
This chapter analyse the essence of a numerical integration within the realm of the Padé approximant (PA) by considering one-dimensional real integral of a univariate function of a real variable in a closed interval. To facilitate a formulation of the numerical integration as a spectral problem, the real variable is replaced by the complex variable and contour integrals are introduced. The error analysis within the PA, or equivalently, the Gaussian quadrature rule can be systematically carried out using the so-called Stieltjes and Geronimus polynomials. Gaussian quadrature rules for certain classes of complex valued weight functions are also possible to construct.
