Asymptotics to all orders of the Hurwitz zeta function

We present several formulae for the large-t asymptotics of the modified Hurwitz zeta function ζ1(x,s),x>0,s=σ+it,0<σ≤1,t>0, which are valid to all orders. In the case of x=0, these formulae are consistent with the asymptotic expressions recently obtained for the Riemann zeta function, which include the classical results of Siegel as a particular case.