  By applying the Euler--Rayleigh methods to a specific representation of the
Jacobi polynomials as hypergeometric functions, we obtain new bounds for their
largest zeros. In particular, we derive upper and lower bound for
$1-x_{nn}^2(\lambda)$, with $x_{nn}(\lambda)$ being the largest zero of the
$n$-th ultraspherical polynomial $P_n^{(\lambda)}$. For every fixed
$\lambda>-1/2$, the limit of the ratio of our upper and lower bounds for
$1-x_{nn}^2(\lambda)$ does not exceed $1.6$. This paper is a continuation of
[1].
