Chebyshev's formula

Chebyshev-Gauss quadrature, also called Chebyshev quadrature, is a Gaussian quadrature over the interval [-1, 1] with weighting function W(x) = (1 - x^2)^(-1/2). The abscissas for quadrature order n are given by the roots of the Chebyshev polynomial of the first kind T_n(x), which occur symmetrically about 0. The weights are w_i | = | -(A_(n + 1) γ_n)/(A_n T_n^, (x_i) T_(n + 1)(x_i)) | = | A_n/A_(n - 1) γ_(n - 1)/(T_(n - 1)(x_i) T_n^, (x_i)), where A_n is the coefficient of x^n in T_n(x), γ_n = A_n π(x),

Gaussian quadrature

Carl Friedrich Gauss | Pafnuty Lvovich Chebyshev