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

Abstract

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