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  • @techreport{RISC4879,
    author = {Fredrik Johansson},
    title = {{Rigorous high-precision computation of the Hurwitz zeta function and its derivatives}},
    language = {english},
    abstract = {We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function $\zeta(s,a)$ for $s, a \in \mathbb{C}$, along with an arbitrary number of derivatives with respect to $s$, to arbitrary precision with rigorous error bounds. Techniques that lead to a fast implementation are discussed. We present new record computations of Stieltjes constants, Keiper-Li coefficients and the first nontrivial zero of the Riemann zeta function, obtained using an open source implementation of the algorithms described in this paper.},
    number = {1309.2877},
    year = {2013},
    institution = {arxiv},
    length = {15}
    }