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

%I A256717 #16 Feb 16 2025 08:33:25
%S A256717 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,
%T A256717 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,
%U A256717 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
%N A256717 Decimal expansion of G(5/4) where G is the Barnes G-function.
%H A256717 G. C. Greubel, <a href="/A256717/b256717.txt">Table of n, a(n) for n = 1..10000</a>
%H A256717 J.-P. Allouche, <a href="http://arxiv.org/abs/1305.6247">A note on products involving zeta(3) and Catalan's constant.</a> arXiv:1305.6247v3 [math.NT], 2013-2014, p. 7.
%H A256717 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>
%H A256717 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A256717 Equals exp(3/32 - Catalan/(4*Pi))*Gamma(1/4)^(1/4)/Glaisher^(9/8).
%F A256717 Equals G(1/4)*Gamma(1/4). - _Vaclav Kotesovec_, Apr 09 2015
%e A256717 1.0650445385309557171597175836949771419373490732697618922213...
%t A256717 RealDigits[BarnesG[5/4], 10, 104] // First
%t A256717 RealDigits[Exp[3/32 - Catalan/(4*Pi)]*Gamma[1/4]^(1/4)/Glaisher^(9/8), 10, 100][[1]] (* _G. C. Greubel_, Aug 25 2018 *)
%o A256717 (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
%Y A256717 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)).
%K A256717 nonn,cons,easy
%O A256717 1,3
%A A256717 _Jean-François Alcover_, Apr 09 2015