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%I #63 May 12 2023 04:20:36
%S 2,0,5,6,1,6,7,5,8,3,5,6,0,2,8,3,0,4,5,5,9,0,5,1,8,9,5,8,3,0,7,5,3,1,
%T 4,8,6,5,2,3,6,8,7,3,7,6,5,0,8,4,9,8,0,4,7,1,6,9,4,4,7,7,8,6,7,1,2,5,
%U 0,9,3,3,8,0,0,4,0,0,1,0,9,2,2,9,2,0,3,6,1,2,5,7,7,4,6,9,8,3,8,1,6,3,0,0,0
%N Decimal expansion of the real part of Li_2(I), negated.
%C This is the decimal expansion of the real part of the dilogarithm of the square root of -1. The imaginary part is Catalan's number (A006752).
%C 5*Pi^2/24 = 10 * (this constant) equals the asymptotic mean of the abundancy index of the even numbers. - _Amiram Eldar_, May 12 2023
%H G. C. Greubel, <a href="/A245058/b245058.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..104 from Robert G. Wilson v)
%F Also equals -zeta(2)/8 = -Pi^2/48.
%F Also equals the Bessel moment Integral_{0..inf} x I_1(x) K_0(x)^2 K_1(x) dx. - _Jean-François Alcover_, Jun 05 2016
%F From _Terry D. Grant_, Sep 11 2016: (Start)
%F Equals Sum_{n>=0} (-1)^n/(2n+2)^2.
%F Equals (Sum_{n>=1} 1/(2n)^2)/2 = A222171/2. (End)
%F Equals Sum_{k>=1} A007949(k)/k^2. - _Amiram Eldar_, Jul 13 2020
%e 0.2056167583560283045590518958307531486523687376508498047169447786712509338004...
%t RealDigits[ Re[ PolyLog[2, I]], 10, 111][[1]] (* or *) RealDigits[ Zeta[2]/8, 10, 111][[1]] (* or *) RealDigits[ Pi^2/48, 10, 111][[1]]
%o (PARI) zeta(2)/8 \\ _Charles R Greathouse IV_, Aug 27 2014
%o (Sage)
%o (pi**2/48).n(200) # _F. Chapoton_, Mar 16 2020
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/48; // _G. C. Greubel_, Aug 25 2018
%Y Cf. A006752, A007949, A072691, A222171, A242301.
%K nonn,cons
%O 0,1
%A _Robert G. Wilson v_, Aug 21 2014
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