cp's OEIS Frontend

A266576 Decimal expansion of Pi^2/12 + log(2)^2 + Sum_{j>=1} 1 / (j^2 * 2^(2*j+1)).

%I A266576 #38 Mar 06 2025 08:18:43
%S A266576 1,4,3,6,7,4,6,3,6,6,8,8,3,6,8,0,9,4,6,3,6,2,9,0,2,0,2,3,8,9,3,5,8,3,
%T A266576 3,5,4,2,4,9,9,5,6,4,3,5,6,5,4,8,7,2,1,0,2,6,6,7,2,4,3,9,2,4,8,6,5,0,
%U A266576 1,5,7,8,9,2,7,7,3,9,7,7,9,7,5,4,3,7,3,7,8,6,7,1,5,5,0,6,8,8,9,0,1,0,1,3,3
%N A266576 Decimal expansion of Pi^2/12 + log(2)^2 + Sum_{j>=1} 1 / (j^2 * 2^(2*j+1)).
%C A266576 A constant related to the asymptotics of A032302.
%H A266576 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dilogarithm.html">Dilogarithm</a>
%H A266576 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>
%H A266576 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>
%F A266576 Equals Pi^2/12 + log(2)^2 + Sum_{j>=1} 1 / (j^2 * 2^(2*j+1)).
%F A266576 Equals Pi^2/6 + log(2)^2/2 + polylog(2, -1/2).
%F A266576 Equals Pi^2/12 + log(2)^2 + polylog(2, 1/4)/2.
%F A266576 Equals -polylog(2, -2). - _Vaclav Kotesovec_, Jul 29 2019
%e A266576 1.436746366883680946362902023893583354249956435654872102667243924865...
%p A266576 evalf(Pi^2/6 + log(2)^2/2 + polylog(2, -1/2), 120);
%p A266576 Digits :=100 ; evalf(dilog(3)) ; # _R. J. Mathar_, Jan 07 2021
%t A266576 RealDigits[Pi^2/12 + Log[2]^2 + PolyLog[2, 1/4]/2,10,120][[1]]
%t A266576 RealDigits[-PolyLog[2, -2], 10, 120][[1]] (* _Vaclav Kotesovec_, Jul 29 2019 *)
%o A266576 (PARI) Pi^2/6 + log(2)^2/2 + polylog(2, -1/2) \\ _Michel Marcus_, Jan 04 2016
%Y A266576 Cf. A032302.
%K A266576 nonn,cons
%O A266576 1,2
%A A266576 _Vaclav Kotesovec_, Jan 04 2016