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A104541 Decimal expansion of lambda(4) in Li's criterion. 7
3, 6, 8, 7, 9, 0, 4, 7, 9, 4, 9, 2, 2, 4, 1, 6, 3, 8, 5, 9, 0, 5, 1, 1, 4, 8, 9, 6, 3, 7, 7, 5, 6, 0, 7, 2, 2, 6, 2, 1, 6, 6, 6, 9, 3, 9, 6, 0, 8, 5, 2, 8, 0, 4, 8, 2, 3, 1, 1, 8, 8, 5, 6, 8, 5, 0, 9, 4, 6, 2, 5, 3, 2, 2, 6, 5, 7, 7, 9, 0, 2, 6, 2, 9, 0, 3, 1, 5, 2, 8, 3, 9, 8, 6, 0, 1, 5, 5, 8, 4, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..101.

Eric Weisstein's World of Mathematics, Li's Criterion

FORMULA

3*Pi^2/4 + Pi^4/96 - 2*log(4) - 2*log(Pi) + 2*gamma - 6*gamma^2 + 4*gamma^3 - gamma^4 - 12*gamma(1) + 12*gamma*gamma(1) - 4*gamma^2*gamma(1) - 2*gamma(1)^2 + 6*gamma(2) - 2*gamma*gamma(2) - 2*gamma(3)/3 - 7*zeta(3)/2 + 1. - Jean-François Alcover, Jul 02 2014

EXAMPLE

0.368790479...

MATHEMATICA

lambda[n_] := Limit[D[s^(n - 1) Log[RiemannXi[s]], {s, n}], s -> 1]/(n - 1)!; RealDigits[N[lambda[4], 110]][[1]][[1 ;; 102]] (* Jean-François Alcover, Oct 31 2012, after Eric W. Weisstein, updated May 18 2016 *)

RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 2 e - 6 e^2 + 4 e^3 - e^4 + 3 Pi^2/4 + Pi^4/96 - 12 g[1] + 12 e g[1] - 4 e^2 g[1] - 2 g[1]^2 + 6 g[2] - 2 e g[2] - 2 g[3]/3 - 2 Log[4 Pi] - 7 Zeta[3]/2], 10, 110][[1]] (* Eric W. Weisstein, Feb 08 2019 *)

CROSSREFS

Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3), A104542 (lambda_5).

Cf. A306339 (lambda_6), A306340 (lambda_7), A306341 (lambda_8).

Sequence in context: A181915 A248760 A011261 * A202300 A244467 A200590

Adjacent sequences:  A104538 A104539 A104540 * A104542 A104543 A104544

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Mar 13 2005

STATUS

approved

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Last modified June 20 19:36 EDT 2019. Contains 324234 sequences. (Running on oeis4.)