A374643 Decimal expansion of 12*Li_2(1/2), where Li_2(z) is the dilogarithm function.

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

Offset: 1

Author

Paolo Xausa, Jul 15 2024

Keywords

• nonn
• cons

Examples

			6.98688631758015007083187584191616130493038169767...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• David Bailey, Peter Borwein, and Simon Plouffe, On the Rapid Computation of Various Polylogarithmic Constants, Mathematics of Computation, Vol. 66, No. 218, April 1997, pp. 903-913.
• 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, Dilogarithm.
• Wikipedia, Dilogarithm.

Crossrefs

Cf. A002388, A076788, A253191, A374641, A374642, A374644.

Programs

Mathematica

First[RealDigits[12*PolyLog[2, 1/2], 10, 100]]

Formula

Equals 12*A076788.

Equals Pi^2 - 6*log(2)^2 = A002388 - 6*A253191 = 12*Sum_{k >= 1} 1/((2^k)*(k^2)). See Bailey et al. (1997), eq. 2.7, p. 906 and Bailey and Crandall (2001), p. 184.