|
| |
|
|
A104539
|
|
Decimal expansion of lambda(2) in Li's criterion.
|
|
16
|
|
|
|
0, 9, 2, 3, 4, 5, 7, 3, 5, 2, 2, 8, 0, 4, 6, 6, 7, 0, 3, 8, 5, 7, 2, 8, 4, 8, 6, 1, 9, 2, 0, 6, 7, 8, 8, 6, 7, 7, 4, 1, 3, 2, 2, 1, 6, 6, 2, 8, 2, 4, 6, 5, 0, 9, 3, 9, 9, 6, 3, 2, 5, 9, 7, 9, 3, 3, 9, 8, 5, 3, 8, 9, 2, 0, 3, 1, 1, 6, 1, 1, 5, 4, 1, 1, 7, 2, 9, 4, 0, 2, 3, 4, 6, 2, 1, 0, 7, 4, 7, 6, 1, 1, 7
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Table of n, a(n) for n=0..102.
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
|
0.0923457352...
|
|
|
MATHEMATICA
|
lambda[n_] := Limit[D[s^(n - 1)*Log[RiemannXi[s]], {s, n}], s -> 1]/(n - 1)!; Join[{0}, RealDigits[lambda[2], 10, 102] // First]
lambda[2] = 1 + EulerGamma - EulerGamma^2 + Pi^2/8 - Log[4 Pi] - 2*StieltjesGamma[1]; Join[{0}, RealDigits[lambda[2], 10, 102] // First] (* Jean-François Alcover, Oct 31 2012, after Eric W. Weisstein, updated May 18 2016 *)
RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + e - e^2 + Pi^2/8 - 2 g[1] - Log[4 Pi]], 10, 110, -1][[1]] (* Eric W. Weisstein, Feb 08 2019 *)
|
|
|
CROSSREFS
|
Cf. A074760 (lambda_1), A104540 (lambda_3), A104541 (lambda_4), A104542 (lambda_5).
Cf. A306339 (lambda_6), A306340 (lambda_7), A306341 (lambda_8).
Sequence in context: A291363 A010161 A222226 * A201559 A300015 A246499
Adjacent sequences: A104536 A104537 A104538 * A104540 A104541 A104542
|
|
|
KEYWORD
|
nonn,cons
|
|
|
AUTHOR
|
Eric W. Weisstein, Mar 13 2005
|
|
|
STATUS
|
approved
|
| |
|
|
