Gaussian quadrature

In numerical analysis, an $n$-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree $2n − 1$ or less by a suitable choice of the nodes $x_i$ and weights $w_i$ for $i = 1, ..., n$.

The modern formulation using orthogonal polynomials was developed by Carl Gustav Jacobi in $1826$.

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