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A114720 Decimal expansion of -(Gamma(1/4)*zeta(1/2))/(8*Pi^(1/4)). 1

%I

%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-Fran├žois 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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Last modified August 2 20:38 EDT 2021. Contains 346428 sequences. (Running on oeis4.)