\[\zeta\left(s,a\right)=\frac{1}{a^{s}}+\frac{1}{(1+a)^{s}}\left(\frac{1}{2}+%
\frac{1+a}{s-1}\right)+\sum_{k=1}^{n}\genfrac{(}{)}{0.0pt}{}{s+2k-2}{2k-1}%
\frac{B_{2k}}{2k}\frac{1}{(1+a)^{s+2k-1}}-\genfrac{(}{)}{0.0pt}{}{s+2n}{2n+1}%
\int_{1}^{\infty}\frac{\widetilde{B}_{2n+1}\left(x\right)}{(x+a)^{s+2n+1}}\,%
\mathrm{d}x,\]