Gaussian Quadrature of int01 f(x) logm(x) dx and int(-1)1 f(x) cos(pi*x/2) dx
Abstract
We tabulate the abscissae and associated weights for numerical integration of integrals with either the singular weight function (-log x)m for exponents m=1, 2 or 3, or the symmetric weight function cos(pi*x/2). Standard brute force arithmetics generates explicit pairs of these values for up to 128 nodes.
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