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A306339
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Decimal expansion of lambda(6) in Li's criterion.
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15
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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, 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, 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
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..109.
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.
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EXAMPLE
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0.8275660122823792974...
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MATHEMATICA
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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]]
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CROSSREFS
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Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3), A104541 (lambda_4).
Cf. A104542 (lambda_5), A306340 (lambda_7), A306341 (lambda_8).
Sequence in context: A317386 A306994 A152179 * A132716 A335004 A134724
Adjacent sequences: A306336 A306337 A306338 * A306340 A306341 A306342
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KEYWORD
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nonn,cons
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AUTHOR
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Eric W. Weisstein, Feb 08 2019
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STATUS
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approved
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