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 A104540 Decimal expansion of lambda(3) in Li's criterion. 16
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS E. Bombieri and J. C. Lagarias, Complements to Li's Criterion for the Riemann Hypothesis, J. Number Th. 77(2) (1999), 274-287. M. W. Coffey, Relations and positivity results for derivatives of the Riemann xi function, J. Comput. Appl. Math. 166(2) (2004), 525-534. Xian-Jin Li, The positivity of a sequence of numbers and the Riemann hypothesis, J. Number Th. 65(2) (1997), 325-333. Eric Weisstein's World of Mathematics, Li's Criterion. Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros. Wikipedia, Li's criterion. FORMULA 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 EXAMPLE 0.207638920... MATHEMATICA 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 *) CROSSREFS Cf. A074760 (lambda_1), A104539 (lambda_2), A104541 (lambda_4), A104542 (lambda_5). Cf. A306339 (lambda_6), A306340 (lambda_7), A306341 (lambda_8). Sequence in context: A351727 A337450 A228819 * A178818 A113319 A298749 Adjacent sequences:  A104537 A104538 A104539 * A104541 A104542 A104543 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Mar 13 2005 STATUS approved

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Last modified June 29 17:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)