We consider the convergence of Gauss-type quadrature formulas for the integral ∫_{x=0...∞} f(x)w(x)dx where w is a weight function on the half line [0,∞). The n-point Gauss-type quadrature formulas are constructed such that they are exact in the set of Laurent polynomials Λ_{-p,q-1} = {∑_{k=-p...q-1} a_k x^k} where p=p(n) is a sequence of integers satisfying 0 ≤ p(n) ≤ 2n and q=q(n)=2n-p(n). It is proved that under certain Carleman-type conditions for the weight and when p(n) or q(n) goes to ∞, then convergence holds for all functions f for which fw is integrable on [0,∞). Some numerical experiments compare the convergence of these quadrature formulas with the convergence of the classical Gauss quadrature formulas for the half line.
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