OFFSET
0,2
LINKS
J. Miller and V. Adamchik, Derivatives of the Hurwitz Zeta Function for Rational Arguments, Journal of Computational and Applied Mathematics 100 (1998) 201-206. [contains a large number of typos]
Eric Weisstein's World of Mathematics, Hurwitz Zeta Function, formula 22.
FORMULA
EXAMPLE
0.053829439326894410047908491727299631045539017902590256244899486116455...
MAPLE
evalf(Zeta(1, -1, 1/2), 120);
evalf(-log(2)/24 - Zeta(1, -1)/2, 120);
MATHEMATICA
RealDigits[Derivative[1, 0][Zeta][-1, 1/2], 10, 120][[1]]
N[With[{k=1}, -BernoulliB[2*k] * Log[2] / 4^k / k - (2^(2*k - 1) - 1) * Zeta'[1 - 2*k] / 2^(2*k - 1)], 120]
PROG
(PARI) zetahurwitz'(-1, 1/2) \\ Michel Marcus, Mar 24 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Mar 23 2019
STATUS
approved