  We present several formulae for the large-$t$ asymptotics of the modified
Hurwitz zeta function $\zeta_1(x,s),x>0,s=\sigma+it,0<\sigma\leq1,t>0,$ which
are valid to all orders. In the case of $x=0$, these formulae reduce to the
asymptotic expressions recently obtained for the Riemann zeta function, which
include the classical results of Siegel as a particular case.
