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arxiv: 1303.5101 · v1 · pith:SGI2OXSLnew · submitted 2013-03-20 · 🧮 math.CA

Gaussian Quadrature of int₀¹ f(x) log^m(x) dx and int_(-1)¹ f(x) cos(pi*x/2) dx

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keywords functionweightabscissaearithmeticsassociatedbruteeitherexplicit
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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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