A258163 Decimal expansion of the log Gamma integral LG_4 = Integral_{0..1} log(Gamma(x))^4 dx.
2, 3, 3, 8, 9, 5, 1, 4, 4, 6, 5, 5, 1, 6, 8, 0, 1, 6, 1, 9, 6, 0, 0, 5, 5, 9, 1, 0, 5, 0, 5, 9, 1, 4, 0, 6, 5, 9, 0, 0, 7, 5, 2, 7, 6, 8, 3, 1, 9, 8, 4, 6, 4, 6, 6, 7, 7, 8, 5, 4, 5, 2, 0, 5, 4, 5, 6, 3, 6, 4, 7, 9, 5, 2, 5, 5, 8, 0, 1, 4, 8, 8, 8, 1, 0, 1, 7, 7, 7, 0, 4, 0, 3, 1, 5, 9, 8, 2, 6, 4, 8, 6, 5, 7, 9
Offset: 2
Examples
23.389514465516801619600559105059140659007527683198464667785452...
Links
- David H. Bailey, David Borwein, and Jonathan M. Borwein, On Eulerian Log-Gamma Integrals and Tornheim-Witten Zeta Functions.
Programs
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Maple
evalf(Int(log(GAMMA(x))^4,x=0..1),120); # Vaclav Kotesovec, May 22 2015
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Mathematica
LG4 = NIntegrate[LogGamma[x]^4, {x, 0, 1}, WorkingPrecision -> 105]; RealDigits[LG4] // First