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A252244 Decimal expansion of zeta''(1/2) (negated).

%I A252244 #10 Feb 16 2025 08:33:24
%S A252244 1,6,0,0,8,3,5,7,0,1,3,9,2,8,6,6,1,4,2,2,6,9,1,3,0,6,5,0,5,9,4,4,9,6,
%T A252244 2,7,8,5,1,8,5,5,9,3,6,1,9,6,3,6,3,5,4,5,3,5,3,0,9,2,9,5,7,5,3,6,6,7,
%U A252244 8,0,9,2,4,6,0,1,4,4,9,8,0,1,3,3,8,0,6,8,0,6,2,7,6,3,5,6,3,8,8,5,5,4,8,4,9
%N A252244 Decimal expansion of zeta''(1/2) (negated).
%H A252244 MathOverflow, <a href="http://mathoverflow.net/questions/129706">Zeta(3) in terms of derivatives of zeta at 1/2 and pi</a>
%H A252244 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>
%H A252244 <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>
%F A252244 zeta(3) = (1/7)*(-Pi^3/4 + (2*zeta'(1/2)^3 - 3*zeta(1/2)*zeta'(1/2)*zeta''(1/2) + zeta(1/2)^2*zeta'''(1/2))/zeta(1/2)^3).
%e A252244 -16.0083570139286614226913065059449627851855936196363545353...
%p A252244 Zeta(2,1/2) ; evalf(%) ;
%t A252244 RealDigits[Zeta''[1/2], 10, 105] // First
%Y A252244 Cf. A002117, A059750, A114875, A252245.
%K A252244 nonn,cons,easy
%O A252244 2,2
%A A252244 _Jean-François Alcover_, Dec 16 2014