A256717 Decimal expansion of G(5/4) where G is the Barnes G-function.

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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

J.-P. Allouche, A note on products involving zeta(3) and Catalan's constant. arXiv:1305.6247v3 [math.NT], 2013-2014, p. 7.

Eric Weisstein's MathWorld, Barnes G-Function

Wikipedia, Barnes G-function

Formula

Equals exp(3/32 - Catalan/(4*Pi))*Gamma(1/4)^(1/4)/Glaisher^(9/8).

Equals G(1/4)*Gamma(1/4). - Vaclav Kotesovec, Apr 09 2015

Example

1.0650445385309557171597175836949771419373490732697618922213...

Mathematica

RealDigits[BarnesG[5/4], 10, 104] // First
RealDigits[Exp[3/32 - Catalan/(4*Pi)]*Gamma[1/4]^(1/4)/Glaisher^(9/8), 10, 100][[1]] (* G. C. Greubel, Aug 25 2018 *)

Prog

(PARI) exp(3/32 - Catalan/(4*Pi))*gamma(1/4)^(1/4)/exp(3/32-9*zeta'(-1)/8) \\ Charles R Greathouse IV, Jul 01 2016

Crossrefs

Cf. A006752 (Catalan), A068466 (Gamma(1/4)), A074962 (Glaisher), A087013 (G(1/4)), A087014 (G(1/2)), A087015 (G(3/4)), A087016 (G(3/2)), A087017 (G(5/2)).

Sequence in context: A197261 A010773 A099288 * A273487 A134103 A196621

Adjacent sequences: A256714 A256715 A256716 * A256718 A256719 A256720

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 09 2015

Status

approved