On the Poincare expansion of the Hurwitz zeta function

In this paper, we extend the result of Paris [R.B. Paris, The Stokes phenomenon associated with the Hurwitz zeta function zeta(s, a), Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461(2053):297-304, 2005] on the exponentially improved expansion of the Hurwitz zeta function zeta(s, z), the expansion of which can be reduced to the large-z Poincare asymptotics of zeta(s, z). Furthermore, we deduce some new series and integral representations of the Hurwitz zeta function zeta(s, z).