  The canonical partition function of a two-dimensional lattice gas in a field
of randomly placed traps, like many other problems in physics, evaluates to the
Gauss hypergeometric function ${}_2F_1(a,b;c;z)$ in the limit when one or more
of its parameters become large. This limit is difficult to compute from first
principles, and finding the asymptotic expansions of the hypergeometric
function is therefore an important task. While some possible cases of the
asymptotic expansions of ${}_2F_1(a,b;c;z)$ have been provided in the
literature, they are all limited by a narrow domain of validity, either in the
complex plane of the variable or in the parameter space. Overcoming this
restriction, we provide new asymptotic expansions for the hypergeometric
function with two large parameters, which are valid for the entire complex
plane of $z$ except for a few specific points. We show that these expansions
work well even when we approach the possible singularity of ${}_2F_1(a,b;c;z)$,
$|z|=1$, where the current expansions typically fail. Using our results we
determine asymptotically the partition function of a lattice gas in a field of
traps in the different possible physical limits of few/many particles and
few/many traps, illustrating the applicability of the derived asymptotic
expansions of the HGF in physics.
