A374644 Decimal expansion of 24*Li_3(1/2), where Li_m(z) is the polylogarithm function.

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

Offset

2,2

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

David H. Bailey and Richard E. Crandall, On the Random Character of Fundamental Constant Expansions, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (preprint draft).

Eric Weisstein's MathWorld, Polylogarithm.

Wikipedia, Polylogarithm.

Formula

Equals 24*A099217.

Equals 4*log(2)^3 + 21*zeta(3) - 2*Pi^2*log(2) = 4*A002162^3 + 21*A002117 - 2*A352769 = 24*Sum_{k >= 1} 1/((2^k)*(k^3)). See Bailey and Crandall (2001), p. 184.

Equals 6 * Intergral_{x>=0} x^2/(exp(x)-1/2) dx. - Amiram Eldar, Jul 06 2026

Example

12.893116646592964822574957414279179840089659984...

Mathematica

First[RealDigits[24*PolyLog[3, 1/2], 10, 100]]

Prog

(PARI) 24 * polylog(3, 1/2) \\ Amiram Eldar, Jul 06 2026

Crossrefs

Cf. A002117, A002162, A002388, A099217, A352769, A374641, A374642, A374643.

Sequence in context: A386934 A155922 A201896 * A154859 A179377 A199274

Adjacent sequences: A374641 A374642 A374643 * A374645 A374646 A374647

Keyword

nonn,cons,changed

Author

Paolo Xausa, Jul 15 2024

Status

approved