A306339 Decimal expansion of lambda(6) in Li's criterion.

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

Offset

0,1

Links

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.

Example

0.8275660122823792974...

Mathematica

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]]

Crossrefs

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

Keyword

nonn,cons

Author

Eric W. Weisstein, Feb 08 2019

Status

approved