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%I #25 Jan 18 2017 02:32:37
%S 6,7,1,7,1,9,6,0,1,8,8,5,8,7,4,5,4,2,3,5,4,4,0,5,0,6,9,2,8,8,7,7,9,8,
%T 8,4,0,0,8,8,0,2,0,6,6,2,1,9,3,5,6,3,3,2,0,5,3,6,1,6,7,3,3,7,5,1,2,5,
%U 1,2,1,7,1,7,5,8,6,1,9,0,2,1,8,3,2,6,7,1,2,6,8,6,2,9,3,2,3,7,2,3,5,5,0,3,6
%N Decimal expansion of the third Malmsten integral: int_{x=1..infinity} log(log(x))/(1 - x + x^2) dx, negated.
%H G. C. Greubel, <a href="/A256128/b256128.txt">Table of n, a(n) for n = 0..5000</a>
%H Iaroslav V. Blagouchine, <a href="http://dx.doi.org/10.1007/s11139-013-9528-5">Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results</a>, The Ramanujan Journal, Volume 35, Issue 1, pp. 21-110, 2014, DOI: 10.1007/s11139-013-9528-5. <a href="http://www.researchgate.net/publication/257381156_Rediscovery_of_Malmsten%27s_integrals_their_evaluation_by_contour_integration_methods_and_some_related_results">PDF file</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Carl_Johan_Malmsten">Carl Malmsten</a>
%F Equals integral_{x=0..1} log(log(1/x))/(1 - x + x^2) dx.
%F Equals integral_{x=0..infinity} log(x)/(1 - 2*cosh(x)) dx.
%F Equals Pi*(7*log(2) + 8*log(Pi) - 3*log(3) - 12*log(Gamma(1/3)))/(3*sqrt(3)).
%e -0.671719601885874542354405069288779884008802066219356...
%p evalf(Pi*(7*log(2)+8*log(Pi)-3*log(3)-12*log(GAMMA(1/3)))/(3*sqrt(3)),120); # _Vaclav Kotesovec_, Mar 17 2015
%t RealDigits[Pi*(7*Log[2]+8*Log[Pi]-3*Log[3]-12*Log[Gamma[1/3]])/(3*Sqrt[3]),10,105][[1]] (* _Vaclav Kotesovec_, Mar 17 2015 *)
%o (PARI) Pi*(7*log(2)+8*log(Pi)-3*log(3)-12*log(gamma(1/3)))/(3*sqrt(3)) \\ _Michel Marcus_, Mar 18 2015
%Y Cf. A115252 (first Malmsten integral), A256127 (second Malmsten integral), A256129 (fourth Malmsten integral), A073005 (Gamma(1/3)), A002162 (log 2), A002391 (log 3), A053510 (log Pi), A002194 (sqrt 3).
%K nonn,cons
%O 0,1
%A _Iaroslav V. Blagouchine_, Mar 15 2015
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