# Laurent series of the Riemann zeta function

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The following Laurent series holds: $$\zeta(z)=\dfrac{1}{z-1} + \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k \lambda_k (z-1)^k}{k!},$$ where $\zeta$ denotes the Riemann zeta function and $\lambda_k$ denotes the Stieltjes constants.