%I #19 Jun 07 2024 11:57:17
%S 5,3,7,2,1,3,1,9,3,6,0,8,0,4,0,2,0,0,9,4,0,6,2,3,2,2,5,5,9,4,9,6,5,8,
%T 2,6,6,7,0,4,0,2,4,9,9,3,4,0,3,7,8,1,7,0,6,8,9,7,6,1,9,3,0,7,1,8,3,2,
%U 4,0,8,0,9,2,0,1,3,8,3,9,7,3,3,0,4,1,2,3,5,9,9,7,5,4,3,9,6,7,0,0,4,8,1,4
%N Decimal expansion of Li_3(1/2).
%D L. Lewin, Polylogarithms and associated Functions, North Holland (1981) A.2.6(3)
%H R. Barbieri, J. A. Mignaco and E. Remiddi, <a href="https://dx.doi.org/10.1007/BF02728545">Electron form factors up to fourth order. I.</a>, Il Nuovo Cim. 11A (4) (1972) 824-864, variable a_3 and table II (15)
%F Li_3(1/2)=sum(k>0, 1/2^k/k^3)=0.537213193608...
%F Li_3(1/2) = 7*zeta(3)/8-Pi^2*log(2)/12+log(2)^3/6. - _Benoit Cloitre_, May 22 2006
%e 0.53721319...
%t RealDigits[ PolyLog[3, 1/2], 10, 104] // First (* _Jean-François Alcover_, Feb 13 2013 *)
%o (PARI) polylog(3,1/2) \\ _Charles R Greathouse IV_, Jul 14 2014
%Y Cf. A076788, A099218, A099219, A099220, A099221, A099222, A099223, A099224.
%K nonn,cons
%O 0,1
%A _Benoit Cloitre_, Oct 06 2004
%E Leading zero removed by _R. J. Mathar_, Feb 05 2009