  We use a Mellin-Barnes integral representation for the Lerch transcendent
$\Phi(z,s,a)$ to obtain large $z$ asymptotic approximations. The simplest
divergent asymptotic approximation terminates in the case that $s$ is an
integer. For non-integer $s$ the asymptotic approximations consists of the sum
of two series. The first one is in powers of $(\ln z)^{-1}$ and the second one
is in powers of $z^{-1}$. Although the second series converges, it is
completely hidden in the divergent tail of the first series. We use resummation
and optimal truncation to make the second series visible.
