(original) (raw)

\[\zeta'\left(1-2n,\tfrac{1}{3}\right)=-\frac{\pi(9^{n}-1)B_{2n}}{8n\sqrt{3}(3^{% 2n-1}-1)}-\frac{B_{2n}\ln 3}{4n\cdot 3^{2n-1}}-\frac{(-1)^{n}{\psi}^{(2n-1)}% \left(\frac{1}{3}\right)}{2\sqrt{3}(6\pi)^{2n-1}}-\frac{\left(3^{2n-1}-1\right% )\zeta'\left(1-2n\right)}{2\cdot 3^{2n-1}},\]