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A306340
Decimal expansion of lambda(7) in Li's criterion.
18
1, 1, 2, 4, 4, 6, 0, 1, 1, 7, 5, 7, 0, 9, 5, 9, 4, 9, 0, 5, 8, 2, 8, 2, 0, 1, 0, 8, 0, 1, 6, 9, 7, 5, 6, 4, 0, 4, 5, 9, 7, 7, 0, 9, 4, 3, 2, 3, 1, 3, 8, 3, 1, 4, 1, 2, 4, 8, 4, 0, 7, 6, 1, 5, 5, 8, 3, 7, 4, 2, 3, 1, 1, 5, 4, 6, 1, 5, 6, 0, 2, 7, 2, 4, 9, 6, 2, 9, 9, 6, 4, 9, 9, 1, 3, 4, 9, 0, 1, 2, 7, 0, 3, 9, 8, 6, 9, 9, 0, 4
OFFSET
1,3
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.
EXAMPLE
1.124460117570959490...
MATHEMATICA
RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 7 e/2 - 21 e^2 + 35 e^3 - 35 e^4 + 21 e^5 - 7 e^6 + e^7 + 21 Pi^2/8 + 35 Pi^4/96 + 7 Pi^6/960 - 42 g[1] + 105 e g[1] - 140 e^2 g[1] + 105 e^3 g[1] - 42 e^4 g[1] + 7 e^5 g[1] - 70 g[1]^2 + 105 e g[1]^2 - 63 e^2 g[1]^2 + 14 e^3 g[1]^2 - 14 g[1]^3 + 7 e g[1]^3 + 105 g[2]/2 - 70 e g[2] + 105/2 e^2 g[2] - 21 e^3 g[2] + 7/2 e^4 g[2] + 105/2 g[1] g[2] - 42 e g[1] g[2] + 21/2 e^2 g[1] g[2] + 7/2 g[1]^2 g[2] - 21 g[2]^2/4 + 7/4 e g[2]^2 - 70 g[3]/3 + 35/2 e g[3] - 7 e^2 g[3] + 7/6 e^3 g[3] - 7 g[1] g[3] + 7/3 e g[1] g[3] + 7/12 g[2] g[3] + 35 g[4]/8 - 7/4 e g[4] + 7/24 e^2 g[4] + 7/24 g[1] g[4] - 7 g[5]/20 + 7/120 e g[5] + 7 g[6]/720 - 7/2 Log[4 Pi] - 245 Zeta[3]/8 - 651 Zeta[5]/32 - 127 Zeta[7]/128], 10, 110][[1]]
CROSSREFS
Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3).
Cf. A104541 (lambda_4), A104542 (lambda_5), A306339 (lambda_6), A306341 (lambda_8).
Sequence in context: A243003 A223227 A160904 * A205969 A326771 A049782
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Feb 08 2019
STATUS
approved