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A386518 Decimal expansion of (log(2*Pi)-1)/2 + gamma.

%I A386518 #18 Jul 24 2025 10:17:19
%S A386518 9,9,6,1,5,4,1,9,8,1,0,6,2,0,5,6,0,2,3,8,6,8,4,1,8,2,6,4,8,8,0,2,0,0,
%T A386518 7,0,9,0,3,5,5,6,8,0,9,5,7,7,7,0,7,0,1,1,6,2,2,9,1,8,7,7,5,3,6,7,6,3,
%U A386518 3,4,2,2,7,0,4,9,2,5,0,6,8,6,3,1,6,9,0,3,6,1,9,2,7,7,0,0,9,4,7,1,3,6,6,3,7,0
%N A386518 Decimal expansion of (log(2*Pi)-1)/2 + gamma.
%C A386518 This is [x^2]G(x), the quadratic coefficient of the Taylor expansion of Barnes' G-function around zero. G(x) = x + this*x^2 -1.114914..*x^3 +O(x^4).
%H A386518 Paolo Xausa, <a href="/A386518/b386518.txt">Table of n, a(n) for n = 0..10000</a>
%H A386518 R. J. Mathar, <a href="https://vixra.org/abs/2507.0094">Erratum to Exercise A4.2 in "An introduction to the theory of the Riemann Zeta Function"</a>, viXra:2507.0094 (2025), coefficient h_2.
%H A386518 Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>
%F A386518 Equals A122914 -1 + A001620.
%e A386518 0.9961541981062056023868418264880200709035568095777...
%p A386518 log(2*Pi)/2-1/2+gamma ; evalf(%) ;
%t A386518 First[RealDigits[(Log[2*Pi] - 1)/2 + EulerGamma, 10, 100]] (* _Paolo Xausa_, Jul 24 2025 *)
%Y A386518 Cf. A122914, A001620.
%K A386518 cons,nonn
%O A386518 0,1
%A A386518 _R. J. Mathar_, Jul 24 2025