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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1985-0771044-5
PII: S 0025-5718(1985)0771044-5
Keywords: Riemann zeta function
Article copyright: © Copyright 1985 American Mathematical Society