Abstract
It is well known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that the shifts ζ(s + iτ ), \( \tau \in \mathbb{R} \) (continuous case), and ζ(s + imh), \( m \in \mathbb{N} \cup \left\{ 0 \right\} \), with fixed h > 0 (discrete case) approximate any analytic function. In the paper, the discrete universality is extended for some classes of the functions F(ζ(s, α)).
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