Remark B:

1. $w(t)=\frac{1}{\sqrt{1-t^{2}}}$ for the Chebyshev polynomials.
2. For $w(t)\equiv 1$ formula (12) is the Gaussian integration formula.
3. Then $\sum\limits _{j=1}^{n}A_{j}=\int\limits _{a}^{b}\mathrm{d}t=b-a,$ i.e. the $A_{j}$ are constant weights (see 2.4).