Summary: Simple bounds depending on \(\alpha\) and \(\beta\) are given for the error term of Hilb formula for Jacobi polynomials \(P_ n^{(\alpha,\beta)} (\cos \theta)\), when \(-1/2 \leq \alpha\), \(\beta \leq 1/2\) and \(0<\vartheta \leq \pi/2\). Under the same hypotheses, new upper bounds are also derived for \(| P_ n^{(\alpha,\beta)} (\cos \theta) |\).