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 $1-x_{nn}^2(��)$, with $x_{nn}(��)$ being the largest zero of the $n$-th ultraspherical polynomial $P_n^{(��)}$. For every fixed $��>-1/2$, the limit of the ratio of our upper and lower bounds for $1-x_{nn}^2(��)$ does not exceed $1.6$. This paper is a continuation of [1].

12 pages, 1 figure