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GaussianQuadratureWeights

GaussianQuadratureWeights[n, a, b]
gives a list of the n pairs {xi, wi} of the elementary n-point Gaussian formula for quadrature on the interval a to b, where wi is the weight of the abscissa xi.
GaussianQuadratureWeights[n, a, b, prec]
attempts to give a result with prec digits of precision.
  • Gaussian quadrature approximates the value of an integral as a linear combination of values of the integrand evaluated at optimal abscissas xi: .
  • The abscissas are optimal in the sense that the quadrature formula is exact for all polynomials up to degree 2n-1.