A306340 Decimal expansion of lambda(7) in Li's criterion.

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

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

1.124460117570959490...

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

Adjacent sequences: A306337 A306338 A306339 * A306341 A306342 A306343

Keyword

nonn,cons

Author

Eric W. Weisstein, Feb 08 2019

Status

approved