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

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, 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, 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

Offset: 0

Author

Eric W. Weisstein, Dec 27 2005

Keywords

• nonn
• cons

Comments

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

Examples

			0.49712077818831410991277373968539771980729360955770518593323423...
		

Links

• Eric Weisstein's World of Mathematics, Xi-Function

Programs

Mathematica

RealDigits[RiemannXi[1/2], 10, 102][[1]] (* Jean-François Alcover, Nov 04 2017 *)

PARI

-(gamma(1/4)*zeta(1/2))/(8*Pi^(1/4)) \\ Michel Marcus, Nov 04 2017

Formula

Equals -(1/4)!*zeta(1/2)/(2*Pi^(1/4)). - Peter Luschny, Jun 27 2021