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To find the Gaussian Quadrature weights and nodes for three points in the interval -1, 1, you typically solve a system of equations based on orthogonal polynomials. For three nodes, the weights and nodes are usually tabulated due to their complexity.
Hmm maybe visit the comment section by "How does a Analysis Algerbra PhD Qualifying Exam look like" from YouTube Channel based "Struggling Grad Student". Or watch his videos... Good luck aoldier.
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