Abstract
In this paper, we extend the result of Paris [R.B. Paris, The Stokes phenomenon associated with the Hurwitz zeta function ζ(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 ζ(s, z), the expansion of which can be reduced to the large-z Poincaré asymptotics of ζ(s, z). Furthermore, we deduce some new series and integral representations of the Hurwitz zeta function ζ(s, z).
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Dedicated to the memory of his teacher and father Xhemail Fejzullahu (1945–2021)
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Fejzullahu, B. On the Poincaré expansion of the Hurwitz zeta function. Lith Math J 61, 460–470 (2021). https://doi.org/10.1007/s10986-021-09527-8
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DOI: https://doi.org/10.1007/s10986-021-09527-8