The article is published in Journal of Computational and Applied Mathematics, 100(1998),201--206.

The functional equation for the Hurwitz Zeta function $\zeta(s, a)$ is used to obtain formulas for derivatives of $\zeta(s, a)$ at negative odd $s$ and rational $a$. For several of these rational arguments, closed form expressions are given in terms of simpler transcendental functions, like the logarithm, the polygamma function, and the Riemann Zeta function.