A087013 Decimal expansion of G(1/4) where G is the Barnes G-function.

2, 9, 3, 7, 5, 5, 9, 6, 5, 3, 3, 8, 6, 0, 9, 9, 5, 4, 7, 1, 7, 6, 8, 1, 6, 1, 0, 3, 2, 0, 5, 4, 6, 1, 7, 6, 6, 2, 0, 6, 2, 5, 3, 5, 9, 6, 7, 9, 8, 4, 3, 0, 5, 0, 1, 4, 9, 5, 7, 8, 9, 8, 8, 6, 3, 3, 3, 9, 6, 0, 4, 3, 0, 4, 0, 8, 7, 5, 0, 2, 2, 7, 3, 6, 1, 0, 2, 7, 2, 4, 3, 3, 2, 7, 3, 7, 4, 8, 4, 9, 5, 7

Offset: 0

Author

Eric W. Weisstein, Jul 30 2003

Keywords

• nonn
• cons

Examples

			0.29375...
		

Links

• Eric Weisstein's World of Mathematics, Barnes G-Function
• Wikipedia, Barnes G-function

Crossrefs

Cf. A087014, A087015, A087016, A087017.

Programs

Mathematica

E^(3/32 - Catalan/(4*Pi))/(Glaisher^(9/8)*Gamma[1/4]^(3/4))
(* Or, since version 7.0, *) RealDigits[BarnesG[1/4], 10, 102] // First (* Jean-François Alcover, Jul 11 2014 *)

PARI

exp(9/8*zeta'(-1)-Catalan/4/Pi)/gamma(1/4)^(3/4) \\ Charles R Greathouse IV, Dec 12 2013

Formula

G(1/4) * G(3/4) = A087013 * A087015 = exp(3/16) / (A^(9/4) * 2^(1/8) * Pi^(1/4) * GAMMA(1/4)^(1/2)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Mar 01 2015