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A104540
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Decimal expansion of lambda(3) in Li's criterion.
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19
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2, 0, 7, 6, 3, 8, 9, 2, 0, 5, 5, 4, 3, 2, 4, 8, 0, 3, 7, 9, 1, 4, 9, 2, 0, 4, 6, 6, 1, 7, 8, 0, 3, 2, 0, 6, 9, 8, 2, 6, 3, 6, 0, 7, 9, 1, 7, 9, 6, 0, 0, 7, 3, 0, 8, 5, 2, 4, 4, 8, 1, 2, 4, 4, 9, 0, 1, 5, 0, 8, 8, 5, 1, 7, 8, 5, 4, 8, 3, 6, 6, 0, 9, 6, 1, 0, 9, 5, 1, 7, 5, 0, 0, 0, 2, 1, 3, 7, 5, 7, 4, 8
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OFFSET
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0,1
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LINKS
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FORMULA
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lambda(3) = 3*Pi^2/8 - 3*log(2) - 3*log(Pi)/2 + 3*gamma/2 - 3*gamma^2 + gamma^3 + 3*gamma*gamma(1) - 6*gamma(1) + 3*gamma(2)/2 - 7*zeta(3)/8 + 1. - Jean-François Alcover, Jul 02 2014
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EXAMPLE
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0.207638920...
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MATHEMATICA
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lambda[n_] := Limit[D[s^(n - 1) Log[RiemannXi[s]], {s, n}], s -> 1]/(n - 1)!; RealDigits[N[lambda[3], 110]][[1]][[1 ;; 102]] (* Jean-François Alcover, Oct 31 2012, after Eric W. Weisstein, updated May 18 2016 *)
RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 3 e/2 - 3 e^2 + e^3 + 3 Pi^2/8 - 6 g[1] + 3 e g[1] + 3 g[2]/2 - Log[8] - 3 Log[Pi]/2 - 7 Zeta[3]/8], 10, 110][[1]] (* Eric W. Weisstein, Feb 08 2019 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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