Positivity of the weights of interpolatory quadrature formulae with Jacobi abscissae (Q698577)

The zeros of the \(n\)th degree Jacobi polynomial \(P_n^{(\alpha, \beta)}\), plus the points \(1\) and \(-1\) are taken as nodes in the interpolatory quadrature formulae, relative to the Legendre weight function \(w(t)=1\) on \([-1,1]\). It is shown that in specific domains of \(\alpha\) and \(\beta\) the weights of these formulae are almost all positive, exceptions occurring only with the weights corresponding to \(1\) and \(-1\).