On the convergence of certain Gauss-type quadrature formulas for unboundedintervals

We consider the convergence of Gauss-type quadrature formulas for the integ ral integral(0)(infinity) f(x)omega(x)dx where omega is a weight function o n the half line [0, infinity). The n-point Gauss-type quadrature formulas a re constructed such that they are exact in the set of Laurent polynomials L ambda(-p,p-1) = {Sigma(k=-p)(q-1) a(k)x(k)}, where p = p(n) is a sequence o f integers satisfying 0 less than or equal to p(n) less than or equal to 2n and q = q(n) = 2n - p(n). It is proved that under certain Carleman-type co nditions for the weight and when p(n) or q(n) goes to infinity, then conver gence holds for all functions f for which f omega is integrable on [0, infi nity). Some numerical experiments compare the convergence of these quadratu re formulas with the convergence of the classical Gauss quadrature formulas for the half line.