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A306341 Decimal expansion of lambda(8) in Li's criterion. 7
1, 4, 6, 5, 7, 5, 5, 6, 7, 7, 1, 4, 7, 0, 6, 0, 6, 3, 2, 6, 5, 5, 5, 1, 4, 5, 4, 1, 9, 7, 7, 7, 4, 8, 7, 8, 7, 9, 1, 9, 8, 4, 7, 8, 6, 1, 8, 7, 4, 5, 4, 4, 4, 6, 5, 8, 4, 5, 8, 5, 7, 7, 5, 3, 8, 3, 5, 7, 9, 5, 0, 2, 8, 5, 2, 3, 5, 6, 3, 7, 9, 4, 4, 7, 8, 1, 1, 5, 1, 7, 5, 5, 6, 0, 3, 8, 0, 6, 9, 0, 0, 1, 2, 5, 0, 1, 5, 1, 8, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..110.

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.

EXAMPLE

1.465755677147060632...

MATHEMATICA

RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 4 e - 28 e^2 + 56 e^3 - 70 e^4 + 56 e^5 - 28 e^6 + 8 e^7 - e^8 + 7 Pi^2/2 + 35 Pi^4/48 + 7 Pi^6/240 + 17 Pi^8/161280 - 56 g[1] + 168 e g[1] - 280 e^2 g[1] + 280 e^3 g[1] - 168 e^4 g[1] + 56 e^5 g[1] - 8 e^6 g[1] - 140 g[1]^2 + 280 e g[1]^2 - 252 e^2 g[1]^2 + 112 e^3 g[1]^2 - 20 e^4 g[1]^2 - 56 g[1]^3 + 56 e g[1]^3 - 16 e^2 g[1]^3 - 2 g[1]^4 + 84 g[2] - 140 e g[2] + 140 e^2 g[2] - 84 e^3 g[2] + 28 e^4 g[2] - 4 e^5 g[2] + 140 g[1] g[2] - 168 e g[1] g[2] + 84 e^2 g[1] g[2] - 16 e^3 g[1] g[2] + 28 g[1]^2 g[2] - 12 e g[1]^2 g[2] - 21 g[2]^2 + 14 e g[2]^2 - 3 e^2 g[2]^2 - 2 g[1] g[2]^2 - 140 g[3]/3 + 140/3 e g[3] - 28 e^2 g[3] + 28/3 e^3 g[3] - 4/3 e^4 g[3] - 28 g[1] g[3] + 56/3 e g[1] g[3] - 4 e^2 g[1] g[3] - 4/3 g[1]^2 g[3] + 14/3 g[2] g[3] - 4/3 e g[2] g[3] - g[3]^2/9 + 35 g[4]/3 - 7 e g[4] + 7/3 e^2 g[4] - 1/3 e^3 g[4] + 7/3 g[1] g[4] - 2/3 e g[1] g[4] - 1/6 g[2] g[4] - 7 g[5]/5 + 7/15 e g[5] - 1/15 e^2 g[5] - 1/15 g[1] g[5] + 7 g[6]/90 - 1/90 e g[6] - g[7]/630 - 4 Log[4 Pi] - 49 Zeta[3] - 217 Zeta[5]/4 - 127 Zeta[7]/16], 10, 110][[1]]

CROSSREFS

Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3), A104541 (lambda_4).

Cf. A104542 (lambda_5), A306339 (lambda_6), A306340 (lambda_7).

Sequence in context: A243396 A140243 A199289 * A306654 A114602 A110000

Adjacent sequences:  A306338 A306339 A306340 * A306342 A306343 A306344

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Feb 08 2019

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)