Formulas for higher derivatives of the Riemann zeta function

Apostol, Tom M.

doi:10.1090/S0025-5718-1985-0771044-5

Formulas for higher derivatives of the Riemann zeta function
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by Tom M. Apostol PDF

Math. Comp. 44 (1985), 223-232 Request permission

Abstract:

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 numerical values are computed to 15D for $k = 0(1)18$.

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