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A258164 Decimal expansion of the log Gamma integral LG_5 = Integral_{0..1} log(Gamma(x))^5 dx. 2

%I

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

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

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

%N Decimal expansion of the log Gamma integral LG_5 = Integral_{0..1} log(Gamma(x))^5 dx.

%H David H. Bailey, David Borwein, Jonathan M. Borwein, <a href="https://www.carma.newcastle.edu.au/jon/log-gamma.pdf">On Eulerian Log-Gamma Integrals and Tornheim-Witten Zeta Functions</a>

%e 118.2987931845512587541672907292964484902928529010820657473411046...

%p evalf(Int(log(GAMMA(x))^5,x=0..1),120); # _Vaclav Kotesovec_, May 22 2015

%t LG5 = NIntegrate[LogGamma[x]^5, {x, 0, 1}, WorkingPrecision -> 105]; RealDigits[LG5] // First

%Y Cf. A075700 (LG_1), A102887 (LG_2), A258162 (LG_3), A258163 (LG_4).

%K nonn,cons,easy

%O 3,3

%A _Jean-Fran├žois Alcover_, May 22 2015

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