A258162 Decimal expansion of the log Gamma integral LG_3 = Integral_{0..1} log(Gamma(x))^3 dx.
5, 7, 4, 0, 3, 8, 8, 8, 0, 7, 2, 2, 9, 4, 7, 4, 2, 8, 0, 0, 1, 9, 5, 7, 1, 6, 8, 8, 1, 0, 2, 4, 6, 1, 4, 6, 2, 9, 6, 1, 0, 1, 3, 0, 0, 7, 4, 5, 4, 8, 7, 3, 3, 3, 1, 4, 2, 5, 4, 0, 2, 4, 5, 1, 2, 3, 8, 8, 8, 4, 3, 8, 7, 1, 7, 7, 1, 2, 5, 0, 2, 6, 1, 0, 6, 2, 6, 2, 1, 6, 6, 6, 2, 8, 7, 2, 3, 3, 0, 5, 1, 5, 7, 8
Offset: 1
Examples
5.7403888072294742800195716881024614629610130074548733314254...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- 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))^3,x=0..1),120); # Vaclav Kotesovec, May 22 2015
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Mathematica
LG3 = NIntegrate[LogGamma[x]^3, {x, 0, 1}, WorkingPrecision -> 104]; RealDigits[LG3] // First -
PARI
intnum(x=0, 1, log(gamma(x))^3) \\ Michel Marcus, Oct 24 2017