Abstract
The question of the convergence of a sequence of product-type quadrature formulas to the integral as the number of nodes becomes unbounded is examined. Conditions on the functions in the integrand and the weights and nodes in the quadrature formulas are stated which insure the convergence of the quadrature process. For example, it is shown that if the functions in the integrand are holomorphic in certain regions of the complex plane which depend upon the nodes used in the quadrature process, then the product-type interpolatory quadrature process converges. Also, necessary and sufficient conditions are given for the convergence of the general product-type quadrature process whenever the functions in the integrand are continuous.
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