(original) (raw)
\[\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k}\zeta\left(nk,a\right)=-n\ln\Gamma\left(a% \right)+\ln\left(\prod_{j=0}^{n-1}\Gamma\left(a-e^{(2j+1)\pi i/n}\right)\right),\]
\[\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k}\zeta\left(nk,a\right)=-n\ln\Gamma\left(a% \right)+\ln\left(\prod_{j=0}^{n-1}\Gamma\left(a-e^{(2j+1)\pi i/n}\right)\right),\]