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%I #17 Jun 28 2021 03:37:32
%S 4,9,7,1,2,0,7,7,8,1,8,8,3,1,4,1,0,9,9,1,2,7,7,3,7,3,9,6,8,5,3,9,7,7,
%T 1,9,8,0,7,2,9,3,6,0,9,5,5,7,7,0,5,1,8,5,9,3,3,2,3,4,2,3,3,9,9,8,4,9,
%U 5,5,2,9,0,4,5,5,4,3,4,8,5,2,3,9,1,6,9,9,6,4,9,7,8,3,8,8,1,4,3,4,9,0
%N Decimal expansion of -(Gamma(1/4)*zeta(1/2))/(8*Pi^(1/4)).
%C Let Xi(s) = -(s + 1/2)*zeta(1/2 - s)*(1/4 - s/2)! / Pi^(1/4 - s/2) be Riemann's (uppercase) Xi function, then the given constant equals Xi(0). - _Peter Luschny_, Jun 28 2021
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Xi-Function.html">Xi-Function</a>
%F Equals -(1/4)!*zeta(1/2)/(2*Pi^(1/4)). - _Peter Luschny_, Jun 27 2021
%e 0.49712077818831410991277373968539771980729360955770518593323423...
%t RealDigits[RiemannXi[1/2], 10, 102][[1]] (* _Jean-François Alcover_, Nov 04 2017 *)
%o (PARI) -(gamma(1/4)*zeta(1/2))/(8*Pi^(1/4)) \\ _Michel Marcus_, Nov 04 2017
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Dec 27 2005
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