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

1,1

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.

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.

Example

6.98688631758015007083187584191616130493038169767...

Mathematica

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

Crossrefs

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

Sequence in context: A198557 A338699 A198214 * A340808 A233589 A199282

Adjacent sequences: A374640 A374641 A374642 * A374644 A374645 A374646

Keyword

nonn,cons

Author

Paolo Xausa, Jul 15 2024

Status

approved