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Decimal expansion of Integral_{0..inf} x log(x)/(exp(x)-1) dx (negated).
1

%I #8 Sep 07 2018 20:31:14

%S 2,4,2,0,9,5,8,9,8,5,8,2,5,9,8,8,4,1,7,7,5,7,2,3,0,3,0,1,5,3,5,4,4,7,

%T 2,2,3,1,8,9,1,6,3,3,6,8,8,1,7,0,1,3,4,2,6,1,3,2,7,2,2,1,8,0,1,7,0,8,

%U 1,6,2,0,1,5,7,7,1,3,3,3,1,4,9,1,0,4,3,4,8,9,9,2,9,8,1,0,2,9,7,5,9

%N Decimal expansion of Integral_{0..inf} x log(x)/(exp(x)-1) dx (negated).

%H G. C. Greubel, <a href="/A273240/b273240.txt">Table of n, a(n) for n = 0..10000</a>

%H Donal F. Connon, <a href="http://arxiv.org/abs/0710.4024">Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume II(b)</a>, arXiv:0710.4024 [math.HO] 2007. page 130.

%F Equals (1/6)*(1-EulerGamma)*Pi^2+zeta'(2).

%F Also equals (1/6)*Pi^2*(1+log(2*Pi)-12*log(G)), where G is the Glaisher-Kinkelin constant.

%e -0.242095898582598841775723030153544722318916336881701342613272218...

%t RealDigits[(1/6) Pi^2 (1 + Log[2Pi] - 12 Log[Glaisher]), 10, 101][[1]]

%o (PARI) default(realprecision, 100); (1/6)*(1-Euler)*Pi^2 + zeta'(2) \\ _G. C. Greubel_, Sep 07 2018

%Y Cf. A001620, A073002, A074962.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, May 18 2016