Also called Radau quadrature. A Gaussian quadrature with weighting function W(x) = 1 in which the endpoints of the interval [-1, 1] are included in a total of n abscissas, giving r = n - 2 free abscissas. Abscissas are symmetrical about the origin, and the general formula is integral_(-1)^1 f(x) d x = w_1 f(-1) + w_n f(1) + sum_(i = 2)^(n - 1) w_i f(x_i). The free abscissas x_i for i = 2, ..., n - 1 are the roots of the polynomial P_(n - 1)^, (x), where P(x) is a Legendre polynomial.

Chebyshev quadrature | Radau quadrature