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x /. FindRoot[x Log[Gamma[x]] - x LogGamma[x] + PolyGamma[-2, x] - 1, {x, 3}, WorkingPrecision -> 120] (* Peter J. C. Moses, June Jun 27 2020 *)
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allocated for Clark KimberlingDecimal expansion of the number x such that 1 = Integral_{0..x} Log(gamma(t)) dt.
2, 7, 5, 5, 0, 1, 6, 8, 5, 6, 6, 9, 0, 4, 8, 4, 8, 6, 8, 7, 9, 2, 9, 0, 5, 5, 0, 7, 4, 8, 1, 4, 7, 3, 6, 9, 0, 7, 5, 0, 0, 5, 9, 7, 5, 4, 6, 3, 7, 0, 4, 6, 4, 4, 1, 4, 4, 7, 9, 8, 8, 2, 7, 9, 5, 0, 2, 5, 5, 5, 3, 4, 5, 3, 5, 2, 4, 3, 1, 0, 7, 1, 7, 4, 3, 5
1,1
x = 2.75501685669048486879290550748147369075005975463704644144...
x /. FindRoot[x Log[Gamma[x]] - x LogGamma[x] + PolyGamma[-2, x] - 1, {x, 3}, WorkingPrecision -> 120] (* Peter J. C. Moses, June 27 2020 *)
Cf. A075700.
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nonn,cons
Clark Kimberling, Jun 27 2020
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allocated for Clark Kimberling
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