Gaussian quadrature with weight function x^2 I would like to get the points and weights of Gaussian quadrature formulas for $$ \int_{-1}^{+1} x^2 f(x)\;\text{d}x. $$ Is this tabulated anywhere yet?

It is not too difficult to derive the coefficients from scratch. The general idea is outlined here.

Up to order 5, the result is:

**n=3:** $$\begin{array}{cc} x_i & w_i\\\\\hline 0 & \frac{8}{75}\\\ \pm \sqrt{\frac{5}7} & \frac{7}{25} \end{array}$$

**n=4:** $$\begin{array}{cc} x_i & w_i\\\\\hline \pm\frac{1}{3} \sqrt{5-2 \sqrt{\frac{10}{7}}} & \frac{1}{300} \left(50-\sqrt{70}\right)\\\ \pm\frac{1}{3} \sqrt{5+2 \sqrt{\frac{10}{7}}} & \frac{1}{300} \left(50+\sqrt{70}\right) \end{array}$$

**n=5:** $$\begin{array}{cc} x_i & w_i\\\\\hline 0 & \frac{128}{3675}\\\ \pm\sqrt{\frac{1}{33} \left(21-2 \sqrt{14}\right)} & \frac{3 \left(258+\sqrt{14}\right)}{4900}\\\ \pm\sqrt{\frac{1}{33} \left(21+2 \sqrt{14}\right)} & \frac{3 \left(258-\sqrt{14}\right)}{4900} \end{array}$$