Gauss–Legendre quadrature

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In numerical analysis, Gauss–Legendre quadrature is a form of Gaussian quadrature for approximating the definite integral of a function. For integrating over the interval [−1, 1], the rule takes the form: ∫ − 1 1 f ( x ) d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} where n is the number of sample points used, wi are quadrature weights, and xi are the roots of the nth Legendre polynomial. This choice of quadrature weights wi and quadrature nodes xi is the unique...

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