Asymptotics to all orders of the Hurwitz zeta function

Arran Fernandez, Athanassios S. Fokas

We present several formulae for the large-$t$ asymptotics of the modified Hurwitz zeta function ${\zeta }_1(x,s),x>0,s=\sigma +it,0<\sigma \le 1,t>0,$ which are valid to all orders. In the case of $x…