Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square $L$-functions II

We prove an asymptotic formula for $F(1\mathrm{/}4-it+ir,1\mathrm{/}4-it-ir,1\mathrm{/}2;x)$ as $r,t\to \mathrm{\infty }$ and $\alpha =r\mathrm{/}t\to 0.$ This special case of the Gauss hypergeometric function appears in the explicit formula for the first moment of Maass form symmetric-square $L$-functions.