OFFSET
0,1
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
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Feb 08 2019
STATUS
approved