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A201995 Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.

%I A201995 #21 Jun 30 2025 04:34:12
%S A201995 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 A201995 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 A201995 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 A201995 Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.
%H A201995 Jason Bard, <a href="/A201995/b201995.txt">Table of n, a(n) for n = 1..2000</a>
%H A201995 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.
%H A201995 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 21.
%F A201995 zeta'''(2)= -Sum_{k>=1} log^3(k)/k^2.
%F A201995 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 A201995 zeta'''(2) = -6.00014580284304486564394121753784..
%p A201995 evalf(Zeta(3,2));
%t A201995 RealDigits[ Zeta'''[2], 10, 93] // First (* _Jean-François Alcover_, Feb 20 2013 *)
%Y A201995 Cf. A013661, A073002, A201994.
%K A201995 cons,nonn
%O A201995 1,1
%A A201995 _R. J. Mathar_, Dec 07 2011