Rational symbolic cubature rules over the first quadrant in a Cartesian plane

In this paper we introduce a new symbolic Gaussian formula for theevaluation of an integral over the first quadrant in Cartesianplane, particular with respect to weight function$w(x)=\exp(-x^T x-1/x^T x)$, where $x=(x_1,x_2)^T\in \mathbb{R}^2_+$. Itintegrates exactly class homogeneous Laurent polynomials withcoefficients commutative field rational functions twovariables. It is derived using connection between orthogonalpolynomials, two-point Padé approximants, and cubatures.We also discuss Padé-typeapproximants order establish cubature formulas ofinterpolatory type. Numerical examples are presented toillustrate different developed paper.