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A086054 Decimal expansion of Pi*log(2).

%I A086054 #47 Feb 16 2025 08:32:50
%S A086054 2,1,7,7,5,8,6,0,9,0,3,0,3,6,0,2,1,3,0,5,0,0,6,8,8,8,9,8,2,3,7,6,1,3,
%T A086054 9,4,7,3,3,8,5,8,3,7,0,0,3,6,9,2,8,6,2,9,4,3,2,5,7,9,5,2,5,3,1,9,4,3,
%U A086054 0,8,5,4,9,1,7,6,7,4,1,9,8,6,4,3,0,3,2,8,9,6,1,6,1,0,6,6,3,0,2,5,0,5,7,6,1
%N A086054 Decimal expansion of Pi*log(2).
%C A086054 Madelung constant b2(2), negated.
%D A086054  G. Boros and V. H. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, 2004 (equation 13.6.6).
%H A086054 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MadelungConstants.html">Madelung Constants</a>
%F A086054 Pi*log(2) = -(8/3)*int(log(x)/sqrt(1+4*x-4*x^2), x=0..1). - _John M. Campbell_, Feb 07 2012
%F A086054 Pi*log(2) = int((x/sin(x))^2, x=0..Pi/2) = int(log(x^2+1)/(x^2+1), x=0..infinity) = int(-log(cos(x)), x=-Pi/2..Pi/2) = int(arctan(1/x)^2, x=0..infinity). - _Jean-François Alcover_, May 30 2013
%F A086054 From _Amiram Eldar_, Jul 11 2020: (Start)
%F A086054 Equals Integral_{x=-1..1} arcsin(x) dx / x.
%F A086054 Equals Integral_{x=-Pi/2..Pi/2} x*cot(x) dx. (End)
%F A086054 Equals Integral_{x = 0..oo} log(x^2 + 4)/(x^2 + 4) dx. - _Peter Bala_, Jul 22 2022
%F A086054 Equals -Im(Polylog(2, 2)). - _Mohammed Yaseen_, Jul 03 2024
%e A086054 2.1775860903036021305006888982376139...
%t A086054 RealDigits[Pi Log[2],10,120][[1]] (* _Harvey P. Dale_, Dec 31 2011 *)
%Y A086054 Cf. A000796 (Pi), A002162 (log(2)), A173623.
%K A086054 nonn,cons,easy
%O A086054 1,1
%A A086054 _Eric W. Weisstein_, Jul 07 2003
%E A086054 Corrected by Antti Ahti (antti.ahti(AT)tkk.fi), Nov 17 2004
%E A086054 More terms from _Benoit Cloitre_, May 21 2005