The FD= and FDHESSIAN= options specify the use of finite difference approximations of the derivatives. The FD= option specifies that all derivatives are approximated using function evaluations, and ...
The functional equation for $\zeta(s)$ is used to obtain formulas for all derivatives $\zeta^{(k)}(s)$. A closed form evaluation of $\zeta^{(k)}(0)$ is given, and ...