# Formula:DLMF:25.11:E7

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${\displaystyle{\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{1}{a^{s}% }+\frac{1}{(1+a)^{s}}\left(\frac{1}{2}+\frac{1+a}{s-1}\right)+\sum_{k=1}^{n}% \binom{s+2k-2}{2k-1}\frac{B_{2k}}{2k}\frac{1}{(1+a)^{s+2k-1}}-\binom{s+2n}{2n+% 1}\int_{1}^{\infty}\frac{\widetilde{B}_{2n+1}\left(x\right)}{(x+a)^{s+2n+1}}% \diffd x}}}$

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