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Mathematics of Computation

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Formulas for higher derivatives of the Riemann zeta function

Author: Tom M. Apostol
Journal: Math. Comp. 44 (1985), 223-232
MSC: Primary 11M06
MathSciNet review: 771044
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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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Keywords: Riemann zeta function
Article copyright: © Copyright 1985 American Mathematical Society