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%I #13 Nov 18 2019 01:26:35
%S 8,2,7,5,6,6,0,1,2,2,8,2,3,7,9,2,9,7,4,2,5,0,0,2,8,2,2,0,2,0,4,9,9,9,
%T 8,1,3,6,8,3,3,7,9,6,4,7,1,9,2,6,9,0,0,5,9,4,0,4,8,5,7,9,6,1,8,9,7,9,
%U 8,3,9,5,0,3,9,3,2,7,7,2,0,8,1,0,3,6,0,6,2,0,1,7,3,9,9,4,5,1,9,2,8,7,9,2,0,0,6,8,3,0
%N Decimal expansion of lambda(6) in Li's criterion.
%H E. Bombieri and J. C. Lagarias, <a href="https://doi.org/10.1006/jnth.1999.2392">Complements to Li's Criterion for the Riemann Hypothesis</a>, J. Number Th. 77(2) (1999), 274-287.
%H M. W. Coffey, <a href="https://doi.org/10.1016/j.cam.2003.09.003">Relations and positivity results for derivatives of the Riemann xi function</a>, J. Comput. Appl. Math. 166(2) (2004), 525-534.
%H Xian-Jin Li, <a href="https://doi.org/10.1006/jnth.1997.2137">The positivity of a sequence of numbers and the Riemann hypothesis</a>, J. Number Th. 65(2) (1997), 325-333.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LisCriterion.html">Li's Criterion</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunctionZeros.html">Riemann Zeta Function Zeros</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Li%27s_criterion">Li's criterion</a>.
%e 0.8275660122823792974...
%t RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 3 e - 15 e^2 + 20 e^3 - 15 e^4 + 6 e^5 - e^6 + 15 Pi^2/8 + 5 Pi^4/32 + Pi^6/960 - 30 g[1] + 60 e g[1] - 60 e^2 g[1] + 30 e^3 g[1] - 6 e^4 g[1] - 30 g[1]^2 + 30 e g[1]^2 - 9 e^2 g[1]^2 - 2 g[1]^3 + 30 g[2] - 30 e g[2] + 15 e^2 g[2] - 3 e^3 g[2] + 15 g[1] g[2] - 6 e g[1] g[2] - 3 g[2]^2/4 - 10 g[3] + 5 e g[3] - e^2 g[3] - g[1] g[3] + 5 g[4]/4 - e g[4]/4 - g[5]/20 - 3 Log[4 Pi] - 35 Zeta[3]/2 - 93 Zeta[5]/16], 10, 110][[1]]
%Y Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3), A104541 (lambda_4).
%Y Cf. A104542 (lambda_5), A306340 (lambda_7), A306341 (lambda_8).
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Feb 08 2019
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