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formula-recurrence: $\eta_n = -(-1)^n \frac{n+1}{n!}\gamma_n + \sum_{k=0}^{n-1} \frac{(-1)^{n-k}}{(n-k-1)!}\eta_k \gamma_{n-k-1}$ for $n\geq 0$, where $\gamma_n$- are the Stieltjes constants. CITE{Cof04}+ are the HREF{Stieltjes_constants}[Stieltjes constants]. CITE{Cof04} formula-log-zeta-1: $\log \zeta(s) = -\log(s-1) - \sum_{n=1}^\infty \frac{\eta_n}{n} (s-1)^n$.
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