We use a Mellin-Barnes integral representation for the Lerch transcendent Φ(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 (lnz)−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
