Number Theory

    

The Hurwitz Zeta Function at the Positive Integers

Authors: Jose Risomar Sousa

A formula for the Hurwitz zeta function at the positive integers k, ζ(k, b), is createdby solving the real and the imaginary parts separately and then combining them. Afew different formulae for the Hurwitz zeta function are known from the literature, butthey are very general and usually hold for ℜ(k) > 1. The advantage of formulae thatonly hold at the positive integers is the fact that they are simpler and easier to workwith. P An analytic continuation of the generating function of ζ(k, b) is also obtained as k≥2 xk(ζ(k, b) − 1/bk), where the term 1/bk was subtracted for convenience.

Comments: 10 Pages.

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[v1] 2026-08-27 21:21:49

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