Laurent Expansion
\zeta(s)=\frac{1}{s-1}+\sum_{k=0}\frac{(-1)^k}{k!}\gamma_k(s-1)^k
The expression for the Laurent Expansion of the Riemann Zeta Function around its pole at s=1 brings to light a connection with the so-called Stieltjes constants that is otherwise hard to see. Key in the demonstration is the Representation by Euler-Maclaurin Formula.
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