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%I #23 Jun 15 2023 02:27:09
%S 3,9,2,2,6,4,6,1,3,9,2,0,9,1,5,1,7,2,7,4,7,1,5,3,1,4,4,6,7,1,4,5,9,9,
%T 5,1,3,7,3,0,3,2,3,9,7,1,5,0,6,5,0,5,2,0,9,5,6,8,2,9,8,4,8,5,2,5,4,7,
%U 2,0,8,0,3,1,5,0,3,3,8,2,8,4,8,8,0,6,5,0,5,2,3,1,0,4,1,4,5,6,9,1,4,0
%N Decimal expansion of -zeta'(1/2).
%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, Table 3.
%H J. Sondow and E. W. Weisstein, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>.
%F Equals ((2*gamma + Pi + 2*log(8*Pi))*zeta(1/2))/4, where gamma is Euler's constant (A001620).
%e 3.92264613920915172747153144671459951373032397150650...
%p Zeta(1,1/2) ;evalf(%) ; # _R. J. Mathar_, May 03 2021
%t RealDigits[-Zeta'[1/2], 10, 120][[1]] (* _Amiram Eldar_, Jun 15 2023 *)
%o (PARI) -zeta'(1/2) \\ _Charles R Greathouse IV_, Mar 28 2012
%o (PARI) -(2*Euler+Pi+2*log(8*Pi))*zeta(1/2)/4 \\ _Charles R Greathouse IV_, Mar 28 2012
%Y Cf. A001620, A059750.
%K nonn,cons
%O 1,1
%A _Eric W. Weisstein_, Jan 03 2006