An approximation of the Hurwitz zeta function by a finite sum - Garunkštis, Ramūnas (Lietuvos matematikos rinkinys, 2003)
We obtain the following version of the approximation of the Hurwitz zeta-function. Let σ ≥ 0 and |t| ≤ π x. Thenζ(s, α) = ∑0 ≤ n ≤ x 1/(n + α)s +{ (x + α)1−s}/(s − 1) + Θ ({7√2π−1 + 3}/xσ).