A252244 - OEIS

%I #9 Mar 19 2024 06:25:34

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

%H MathOverflow, <a href="http://mathoverflow.net/questions/129706">Zeta(3) in terms of derivatives of zeta at 1/2 and pi</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%H <a href="/wiki/Index_to_constants#Start_of_section_Z">Index entries for constants related to zeta</a>

%F 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 -16.0083570139286614226913065059449627851855936196363545353...

%p Zeta(2,1/2) ; evalf(%) ;

%t RealDigits[Zeta''[1/2], 10, 105] // First

%Y Cf. A002117, A059750, A114875, A252245.

%K nonn,cons,easy

%O 2,2

%A _Jean-François Alcover_, Dec 16 2014