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

0,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 44.

Leonard Lewin, Polylogarithms and associated Functions, North Holland (1981), A.2.6(3).

Links

Table of n, a(n) for n=0..103.

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

Equals Sum_{k>0} 1/(2^k*k^3).

Equals 7*zeta(3)/8 - Pi^2*log(2)/12 + log(2)^3/6. - Benoit Cloitre, May 22 2006

From Amiram Eldar, Jun 25 2026: (Start)

Equals (1/4) * Intergral_{x>=0} x^2/(exp(x)-1/2) dx.

Equals Intergral_{x=0..1} log(x)*log(1-x/2)/x dx. (End)

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

Crossrefs

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

Sequence in context: A066253 A065169 A247617 * A023103 A153454 A198877

Adjacent sequences: A099214 A099215 A099216 * A099218 A099219 A099220

Keyword

nonn,cons,changed

Author

Benoit Cloitre, Oct 06 2004

Extensions

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

Status

approved