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).

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