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%I #19 Aug 11 2019 13:49:20
%S 0,0,4,9,1,0,9,2,5,6,4,7,7,6,0,8,3,2,3,5,2,7,3,9,1,5,0,9,2,3,6,1,5,1,
%T 8,6,0,3,2,4,8,4,2,9,7,4,1,7,6,9,2,9,4,5,9,7,7,9,6,1,6,5,7,5,2,8,0,3,
%U 0,6,3,1
%N Decimal expansion of the Dickman function evaluated at 1/4.
%C Density of the fourth-root-smooth numbers.
%D Karl Dickman, On the frequency of numbers containing prime factors of a certain relative magnitude, Arkiv för Matematik, Astronomi och Fysik 22A 10 (1930), pp. 1-14.
%H David Broadhurst, <a href="http://arxiv.org/abs/1004.0519">Dickman polylogarithms and their constants</a> arXiv:1004.0519 [math-ph], 2010.
%e F(1/4) = 0.00491092564776083235273915092361518603248429741769294597796...
%t RealDigits[1-Log[4]+PolyLog[2, 1/4]+2*Log[2]^2-Pi^2/12-PolyLog[3, 1/4]-PolyLog[2, 1/4]*Log[2]-2/3*Log[2]^3+13*Zeta[3]/24,10,100,-1][[1]] (* _Vaclav Kotesovec_, Jul 15 2014 *)
%o (PARI) 1-log(4)+polylog(2,1/4)+2*log(2)^2-Pi^2/12-polylog(3,1/4)-polylog(2,1/4)*log(2)-2/3*log(2)^3+13*zeta(3)/24
%Y F(1/2) = A244009, F(1/3) = A175475.
%K nonn,cons
%O 0,3
%A _Charles R Greathouse IV_, Jul 14 2014
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