  In (Boyd, Proc. R. Soc. Lond. A 447 (1994) 609--630), W. G. C. Boyd derived a
resurgence representation for the gamma function, exploiting the reformulation
of the method of steepest descents by M. Berry and C. Howls (Berry and Howls,
Proc. R. Soc. Lond. A 434 (1991) 657--675). Using this representation, he was
able to derive a number of properties of the asymptotic expansion for the gamma
function, including explicit and realistic error bounds, the smooth transition
of the Stokes discontinuities, and asymptotics for the late coefficients. The
main aim of this paper is to modify the resurgence formula of Boyd making it
suitable for deriving better error estimates for the asymptotic expansions of
the gamma function and its reciprocal. We also prove the exponentially improved
versions of these expansions complete with error terms. Finally, we provide new
(formal) asymptotic expansions for the coefficients appearing in the asymptotic
series and compare their numerical efficacy with the results of earlier
authors.
