Asymptotics to all orders of the Hurwitz zeta function

作者：Fernandez Arran; Fokas Athanassios S

来源：Journal of Mathematical Analysis and Applications, 2018, 465(1): 423-458.

DOI：10.1016/j.jmaa.2018.05.012

• Hurwitz zeta function
• Asymptotic series

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 <= 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.

• 出版日期2018-9-1