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