A099217 Decimal expansion of Li_3(1/2).

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

Author

Benoit Cloitre, Oct 06 2004

Keywords

• nonn
• cons

Examples

			0.537213193608040200940623225594965826670402499340...
		

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.

Crossrefs

Cf. A076788, A099218, A099219, A099220, A099221, A099222, A099223, A099224.

Programs

Mathematica

RealDigits[PolyLog[3, 1/2], 10, 104] // First (* Jean-François Alcover, Feb 13 2013 *)

PARI

polylog(3,1/2) \\ Charles R Greathouse IV, Jul 14 2014

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

Extensions

Leading zero removed by R. J. Mathar, Feb 05 2009