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Formulas for Higher Derivatives of the Riemann Zeta Function

Tom M. Apostol
Mathematics of Computation
Vol. 44, No. 169 (Jan., 1985), pp. 223-232
DOI: 10.2307/2007806
Stable URL: http://www.jstor.org/stable/2007806
Page Count: 10
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Formulas for Higher Derivatives of the Riemann Zeta Function
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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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