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 \( N\rightarrow \infty \).