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We revisit the problem of extending quadrature formulas for general weightfunctions, and provide a generalization of Patterson's method for the constantweight function. The method can be used to compute a nested sequence ofquadrature formulas for integration with respect to any continuous probabilitymeasure on the real line with finite moments. The advantages of the methodinclude that it works directly with the moments of the underlying distribution,and that for distributions with rational moments the existence of the formulascan be verified by exact rational arithmetic.

Generating nested quadrature formulas for general weight functions with known moments