A099218 Decimal expansion of Li_4(1/2).

5, 1, 7, 4, 7, 9, 0, 6, 1, 6, 7, 3, 8, 9, 9, 3, 8, 6, 3, 3, 0, 7, 5, 8, 1, 6, 1, 8, 9, 8, 8, 6, 2, 9, 4, 5, 6, 2, 2, 3, 7, 7, 4, 7, 5, 1, 4, 1, 3, 7, 9, 2, 5, 8, 2, 4, 4, 3, 1, 9, 3, 4, 7, 9, 7, 7, 0, 0, 8, 2, 8, 1, 5, 8, 1, 8, 6, 4, 9, 7, 6, 9, 3, 6, 4, 8, 5, 7, 7, 7, 8, 2, 6, 5, 6, 0, 9, 0, 0, 6, 4, 7, 7, 2

Offset

0,1

References

Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), Section 1.3.2.

Links

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

George Rutledge and R. D. Douglass, Table of definite integrals, Am. Math. Monthly 45 (8) (1938), 525-530, eq. (22).

Formula

Equals Sum_{k>0} 1/(2^k*k^4).

From Amiram Eldar, Jun 25 2026: (Start)

Equals (1/12) * Intergral_{x>=0} x^3/(exp(x)-1/2) dx.

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

Example

0.51747906167389938633075816189886294562237747514137...

Maple

polylog(4, 1/2) ; evalf(%) ; # R. J. Mathar, Feb 15 2013

Mathematica

RealDigits[ N[ PolyLog[4, 1/2], 104]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

Prog

(PARI) polylog(4, 1/2) \\ Charles R Greathouse IV, Jul 14 2014

Crossrefs

Cf. A076788, A099217, A099219, A099220, A099221, A099222, A099223, A099224.

Sequence in context: A322050 A370516 A021663 * A198129 A244425 A332343

Adjacent sequences: A099215 A099216 A099217 * A099219 A099220 A099221

Keyword

cons,nonn,changed

Author

Benoit Cloitre, Oct 06 2004

Extensions

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

Status

approved