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A103130 Decimal expansion of Integrate[(1 - x)/((1 + x y) (Log[x y])^2),{y,0,1},{x,0,1}].

%I A103130 #24 Feb 16 2025 08:32:56
%S A103130 2,5,6,2,2,0,0,9,4,4,7,4,1,3,6,1,3,4,7,0,1,7,9,4,1,6,2,0,9,8,6,7,3,8,
%T A103130 8,2,9,8,6,4,4,8,8,6,5,0,4,8,5,6,8,6,9,1,2,8,1,8,1,8,6,9,6,1,3,7,9,3,
%U A103130 4,5,2,3,9,7,7,2,3,2,2,4,1,5,7,5,4,5,5,0,2,2,3,0,3,6,4,2,2,5,1,6,1,5
%N A103130 Decimal expansion of Integrate[(1 - x)/((1 + x y) (Log[x y])^2),{y,0,1},{x,0,1}].
%C A103130 Equals Integral_{u=0..1} (u - log(u) - 1)/((1 + u)*(log(u))^2). (Let u = x*y and v = y, and integrate w.r.t. v.) - _Petros Hadjicostas_, Jun 13 2020
%H A103130 G. C. Greubel, <a href="/A103130/b103130.txt">Table of n, a(n) for n = 0..5000</a>
%H A103130 Jonathan Sondow, <a href="https://arxiv.org/abs/math/0211148">Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula</a>, arXiv:math/0211148 [math.CA], 2002-2004.
%H A103130 Jonathan Sondow, <a href="http://www.jstor.org/stable/30037385">Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula</a>, Amer. Math. Monthly 112 (2005), 61-65.
%H A103130 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HadjicostassFormula.html">Hadjicostas's Formula</a>.
%F A103130 Log[(Sqrt[Pi]*Glaisher^6)/(2^(7/6)*E)].
%e A103130 0.256220094...
%t A103130 RealDigits[Log[(Sqrt[Pi]*Glaisher^6)/(2^(7/6)*E)], 10, 50][[1]] (* _G. C. Greubel_, Mar 16 2017 *)
%Y A103130 Cf. A094640.
%K A103130 nonn,cons
%O A103130 0,1
%A A103130 _Eric W. Weisstein_, Jan 23 2005