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Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.
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%I #16 Oct 25 2021 16:06:54

%S 6,0,0,0,1,4,5,8,0,2,8,4,3,0,4,4,8,6,5,6,4,3,9,4,1,2,1,7,5,3,7,8,4,8,

%T 3,8,3,7,4,0,5,8,8,6,1,5,9,4,4,5,6,8,5,8,5,0,3,5,1,0,7,9,5,0,0,8,5,9,

%U 7,4,1,6,7,4,7,5,1,0,0,3,5,9,2,4,1,5,0,3,4,2,5,6,0

%N Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.

%H B. K. Choudhury, <a href="https://doi.org/10.1098/rspa.1995.0096">The Riemann zeta-function and its derivatives</a>, Proc. R. Soc. Lond A 445 (1995) 477-499.

%F zeta'''(2)= -Sum_{k>=1} log^3(k)/k^2.

%F Equals 3! + Sum_{k>=0} (-1)^k*gamma(3+k)/k!, where gamma(.) are the Stieltjes constants A001620, A082633, A086279 etc. [Choudhury, Thm. 4]

%e zeta'''(2) = -6.00014580284304486564394121753784..

%p evalf(Zeta(3,2));

%t RealDigits[ Zeta'''[2], 10, 93] // First (* _Jean-François Alcover_, Feb 20 2013 *)

%Y Cf. A013661, A073002, A201994.

%K cons,nonn

%O 1,1

%A _R. J. Mathar_, Dec 07 2011