Sums of zeta^{(n)}(rho) over non-trivial zeros rho admit a full asymptotic expansion whose leading term is real and positive for odd n, negative for even n.
The Laurent expansion of the Riemann zeta function
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A discrete mean-value theorem for the higher derivatives of the Riemann zeta function
Sums of zeta^{(n)}(rho) over non-trivial zeros rho admit a full asymptotic expansion whose leading term is real and positive for odd n, negative for even n.