I came across the statement $$\sum_{n>x}^\infty n^{-s}=\int_x^\infty u^{-s}d[u]$$ (where $s\in\mathbb{C}\setminus\{1\}, Re(s)>0, x>0$). However, I have trouble understanding the integral. How do you handle the differential $d[u]$?
2026-04-02 04:25:53.1775103953
Integer part as variable of integration
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