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A104542 Decimal expansion of lambda(5) in Li's criterion. 7
5, 7, 5, 5, 4, 2, 7, 1, 4, 4, 6, 1, 1, 7, 7, 4, 5, 2, 4, 3, 1, 1, 0, 6, 4, 0, 5, 4, 9, 2, 8, 6, 3, 8, 3, 3, 5, 6, 7, 4, 5, 6, 6, 1, 5, 1, 7, 9, 7, 9, 9, 5, 3, 9, 5, 2, 9, 2, 4, 7, 5, 8, 1, 9, 3, 5, 9, 5, 4, 5, 2, 1, 3, 8, 3, 6, 2, 3, 6, 4, 0, 7, 8, 1, 9, 0, 1, 6, 3, 1, 0, 0, 5, 4, 8, 5, 8, 9, 4, 7, 2, 3 (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

lambda(5) = 5*Pi^2/4 + 5*Pi^4/96 - 5*log(4)/2 - 5*log(Pi)/2 + 5*gamma/2 - 10*gamma^2 + 10*gamma^3 - 5*gamma^4+gamma^5 - 20*gamma(1) + 30*gamma*gamma(1) - 20*gamma^2*gamma(1) + 5*gamma^3*gamma(1) - 10*gamma(1)^2 + 5*gamma*gamma(1)^2 + 15*gamma(2) - 10*gamma*gamma(2) + 5/2*gamma^2*gamma(2) + 5/2*gamma(1)*gamma(2) - 10*gamma(3)/3 + 5/6*gamma*gamma(3) + 5*gamma(4)/24 - 35*zeta(3)/4 - 31*zeta(5)/32+1. - Jean-François Alcover, Jul 02 2014

EXAMPLE

0.575542714...

MATHEMATICA

lambda[n_] := Limit[D[s^(n - 1)*Log[xi[s]], {s, n}], s -> 1]/(n - 1)!; RealDigits[N[lambda[5], 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 + 5 e/2 - 10 e^2 + 10 e^3 - 5 e^4 + e^5 + 5 Pi^2/4 + (5 Pi^4)/96 - 20 g[1] + 30 e g[1] - 20 e^2 g[1] + 5 e^3 g[1] - 10 g[1]^2 + 5 e g[1]^2 + 15 g[2] - 10 e g[2] + 5/2 e^2 g[2] + 5/2 g[1] g[2] - 10 g[3]/3 + 5/6 e g[3] + 5 g[4]/24 - Log[32] - 5 Log[Pi]/2 - 35 Zeta[3]/4 - 31 Zeta[5]/32], 10, 110][[1]] (* Eric W. Weisstein, Feb 08 2019 *)

CROSSREFS

Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3), A104541 (lambda_4).

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

Sequence in context: A198744 A201944 A165242 * A161376 A107437 A317083

Adjacent sequences:  A104539 A104540 A104541 * A104543 A104544 A104545

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Mar 13 2005

STATUS

approved

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Last modified June 25 23:52 EDT 2019. Contains 324367 sequences. (Running on oeis4.)