A087015 Decimal expansion of G(3/4) where G is the Barnes G-function.

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

Offset: 0

Author

Eric W. Weisstein, Jul 30 2003

Keywords

• nonn
• cons

Examples

			0.84871...
		

Links

• Junesang Choi, H. M. Srivastava, Certain classes of series involving the Zeta Function, J. Math. Anal. Applic. 231 (1999) 91-117
• Eric Weisstein's World of Mathematics, Barnes G-Function
• Wikipedia, Barnes G-function

Crossrefs

Cf. A087013, A087014, A087016, A087017.

Programs

Mathematica

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

PARI

exp(Catalan/4/Pi+9/8*zeta'(-1))/gamma(3/4)^(1/4) \\ 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