Rigorous high-precision computation of the Hurwitz zeta function and its derivatives

Abstract

We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function ζ(s, a) for s , a ∈ ℂ $s, a \in \mathbb {C}$ , 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… (More)
DOI: 10.1007/s11075-014-9893-1

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