Asymptotic formulas for zero-balanced hypergeometric series

A hypergeometric series is called $s$-balanced if the sum of denominator parameters minus the sum of numerator parameters is $s$. A nonterminating $s$-balanced hypergeometric series converges at $x = 1$ if $s$ is positive. An asymptotic formula for the partial sums of a zero-balanced _3 F_2 (1)$ is given. A corollary is the behavior of a zero-balanced _3 F_2 (x)$ as $x$ approaches 1. Some $q$-analogues are also given.