The quadrature weights or just weights (not to be confused with the weight function) are positive and the sequence of Gaussian quadrature formulae is convergent if the sequence $Q_N$ of quadrature formulae $$\begin{equation*} Q_N(f)\rightarrow Q(f)=\int_a^bf(x)dx, \end{equation*}$$ in the limit $N\rightarrow \infty$.