Gauss-Laguerre quadrature | Laguerre quadrature

Laguerre-Gauss quadrature, also called Gauss-Laguerre quadrature or Laguerre quadrature, is a Gaussian quadrature over the interval [0, ∞) with weighting function W(x) = e^(-x). It fits all polynomials of degree 2m - 1 exactly. The abscissas for quadrature order n are given by the roots of the Laguerre polynomials L_n(x). The weights are w_i | = | -(A_(n + 1) γ_n)/(A_n L_n^, (x_i) L_(n + 1)(x_i)) | = | A_n/A_(n - 1) γ_(n - 1)/(L_(n - 1)(x_i) L_n^, (x_i)), where A_n is the coefficient of x^n in L_n(x).

Gaussian quadrature

Carl Friedrich Gauss | Edmond Nicolas Laguerre