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

Author

Paolo Xausa, Jul 15 2024

Keywords

• nonn
• cons

Examples

			12.893116646592964822574957414279179840089659984...
		

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.

Crossrefs

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

Programs

Mathematica

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

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.