Integration points and weights with orthogonal polynomials
We have then
$$
\begin{equation*}
Q_{N-1}(\hat{x}_k) = \hat{L}\hat{\alpha},
\end{equation*}
$$
yielding (if \( \hat{L} \) has an inverse)
$$
\begin{equation*}
\hat{L}^{-1}Q_{N-1}(\hat{x}_k) = \hat{\alpha},
\end{equation*}
$$
which is Eq.
(17).