|
%I #20 May 10 2021 04:55:41
%S 0,4,8,6,0,8,3,8,8,2,9,1,1,3,1,5,6,6,9,0,7,1,8,3,0,3,9,3,4,3,4,0,7,4,
%T 2,1,3,5,4,3,2,9,5,8,0,4,7,8,1,4,0,5,4,2,3,1,6,8,0,5,2,8,5,0,5,1,4,8,
%U 8,2,3,5,7,3,5,9,3,2,4,7,2,0,0,4,0,9,1,2,9,3,3,7,1,1,6,7,7,0,7,9,6,8,0,4,4
%N Decimal expansion of the Dickman function evaluated at 1/3.
%C Density of the cube root-smooth numbers, see A090081. - _Charles R Greathouse IV_, Jul 14 2014
%H David Broadhurst, <a href="http://arxiv.org/abs/1004.0519">Dickman polylogarithms and their constants</a> arXiv:1004.0519 [math-ph], 2010.
%H K. Soundararajan, <a href="http://arxiv.org/abs/1005.3494">An asymptotic expansion related to the Dickman function</a>, arXiv:1005.3494 [math.NT], 2010.
%F Equals 1 - log(3) + log^2(3)/2 - Pi^2/12 + Sum_{n>=1} 1/(n^2*3^n), where Sum_{n>=1} 1/(n^2*3^n) = 0.3662132299770634876167462976642627638...
%e F(1/3) = 0.04860838829113156690718...
%t N[1 - Log[3] + Log[3]^2/2 - Pi^2/12 + PolyLog[2, 1/3], 105] // RealDigits // First // Prepend[#, 0]& (* _Jean-François Alcover_, Feb 05 2013 *)
%o (PARI) 1-log(3)+log(3)^2/2-Pi^2/12+polylog(2,1/3) \\ _Charles R Greathouse IV_, Jul 14 2014
%Y Cf. A002391, A072691, A175478.
%K cons,nonn
%O 0,2
%A _R. J. Mathar_, May 25 2010
|
