A374643 - OEIS

%I #30 Jul 19 2024 02:27:01

%S 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,

%T 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,

%U 5,2,5,2,8,8,6,0,1,9,8,4,0,9,8,0,2,0,8,3,8,2

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

%H Paolo Xausa, <a href="/A374643/b374643.txt">Table of n, a(n) for n = 1..10000</a>

%H David Bailey, Peter Borwein, and Simon Plouffe, <a href="https://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf">On the Rapid Computation of Various Polylogarithmic Constants</a>, Mathematics of Computation, Vol. 66, No. 218, April 1997, pp. 903-913.

%H David H. Bailey and Richard E. Crandall, <a href="https://doi.org/10.1080/10586458.2001.10504441">On the Random Character of Fundamental Constant Expansions</a>, Experimental Mathematics, Vol. 10 (2001), Issue 2, pp. 175-190 (<a href="https://www.davidhbailey.com/dhbpapers/baicran.pdf">preprint draft</a>).

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Dilogarithm.html">Dilogarithm</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dilogarithm">Dilogarithm</a>.

%F Equals 12*A076788.

%F 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.

%e 6.98688631758015007083187584191616130493038169767...

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

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

%K nonn,cons

%O 1,1

%A _Paolo Xausa_, Jul 15 2024