I'm looking for a list of values for ${\xi^{(n)}(\frac{1}{2})}$, where $\xi^{(n)}$ is the $n^{\text{th}}$ derivative of the Riemann's $\xi$ function or, alternatively, some implementation of ${\xi^{(n)}(s)}$, eventually in Mathematica.
Thanks in advance.
For computing $\xi^{(2n)}(1/2)$ for only one $n$ you should use $$\xi(s) =\frac{s (s-1)}{2} \Lambda(s)$$ where $$\Lambda(s)= \Gamma(s/2)\pi^{-s/2} \zeta(s)= \int_0^\infty (\theta(x)-1) x^{s/2-1}dx\qquad\qquad \\ \qquad = \frac{1}{s-1}-\frac{1}{s}+\int_1^\infty (x^{s/2-1}+x^{(1-s)/2-1})(\theta(x)-1)dx \\ \theta(x) = \sum_{n=-\infty}^\infty e^{-\pi n^2 x} = x^{-1/2} \theta(1/x)\qquad\qquad\qquad\qquad\qquad$$
Also why would you need $\xi^{(2n)}(1/2)$ ?