The present paper is a continuation of an earlier work (see the paper reviewed above). The monotonicity condition of the sequence \(\{\beta_ n\}\) is given up. The result is applied to the measures \(d\mu(x)=(1-x^ 2)^ \alpha| x|^{2\beta+1}dx\) and \(d\mu(x)=| x|^{2\alpha+1} e^{-x^ 2}dx\), \(\alpha,\beta>-1\). As a corollary, a Gasper result is derived on the Jacobi polynomials \(P^{(\alpha,\beta)}_ n\) with \(\alpha\geq \beta\) and \(\alpha+\beta+1\geq 0\).