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A099217
Decimal expansion of Li_3(1/2).
8
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, 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, 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
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 44.
L. Lewin, Polylogarithms and associated Functions, North Holland (1981) A.2.6(3)
LINKS
R. Barbieri, J. A. Mignaco, and E. Remiddi, Electron form factors up to fourth order. I, Il Nuovo Cim. 11A (4) (1972) 824-864, variable a_3 and table II (15).
Michael I. Shamos, A catalog of the real numbers, (2007). See p. 473.
FORMULA
Li_3(1/2) = Sum_{k>0} 1/(2^k*k^3) = 0.537213193608...
Li_3(1/2) = 7*zeta(3)/8-Pi^2*log(2)/12+log(2)^3/6. - Benoit Cloitre, May 22 2006
EXAMPLE
0.537213193608040200940623225594965826670402499340...
MATHEMATICA
RealDigits[PolyLog[3, 1/2], 10, 104] // First (* Jean-François Alcover, Feb 13 2013 *)
PROG
(PARI) polylog(3, 1/2) \\ Charles R Greathouse IV, Jul 14 2014
KEYWORD
nonn,cons,changed
AUTHOR
Benoit Cloitre, Oct 06 2004
EXTENSIONS
Leading zero removed by R. J. Mathar, Feb 05 2009
STATUS
approved