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%I #62 Sep 08 2022 08:45:59
%S 3,2,8,9,8,6,8,1,3,3,6,9,6,4,5,2,8,7,2,9,4,4,8,3,0,3,3,3,2,9,2,0,5,0,
%T 3,7,8,4,3,7,8,9,9,8,0,2,4,1,3,5,9,6,8,7,5,4,7,1,1,1,6,4,5,8,7,4,0,0,
%U 1,4,9,4,0,8,0,6,4,0,1,7,4,7,6,6,7,2,5,7,8,0,1,2,3,9,5,1,7,4,1,0,6,0,8,0,0
%N Decimal expansion of Pi^2/3.
%D Marc Briane and Gilles Pagès, Théorie de l'Intégration, Vuibert, 2004, 3ème édition, exercice 12.15, p. 256.
%H George E. Andrews, <a href="https://doi.org/10.1073/pnas.0500218102">Partitions with short sequences and mock theta functions</a>, Proceedings of the National Academy of Sciences, Vol. 102, No. 13 (2005), pp. 4666-4671.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 3 + A145426.
%F Equals -Sum_{n>=1} Psi_2(n), where Psi_2 is the tetragamma function. - _Istvan Mezo_, Oct 25 2012
%F Equals Integral_{x=0..1} (log(x)/(x - 1))^2 dx. - _Jean-François Alcover_, Mar 21 2013
%F Equals Integral_{x=-oo..oo} x^2/sinh(x)^2 dx. - _Amiram Eldar_, Aug 06 2020
%F Equals Integral_{x=0..oo} (log(x+1)/x)^2 dx (reference Briane and Pagès). - _Bernard Schott_, Feb 13 2022
%e 3.289868133696452872944830333292050378438...
%t RealDigits[Pi^2/3, 10, 105][[1]] (* _T. D. Noe_, Oct 05 2011 *)
%o (Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^105*pi^2/3))); // _Vincenzo Librandi_, Jan 12 2016
%o (PARI) 2*zeta(2) \\ _Charles R Greathouse IV_, Jan 20 2022
%o (PARI) sumnumrat(1/x^2,-oo) \\ _Charles R Greathouse IV_, Jan 20 2022
%Y Cf. A002388, A102753, A091476, 2*A013661, A164102.
%Y Cf. A024916 (partial sums of A000203).
%K nonn,cons
%O 1,1
%A _Omar E. Pol_, Oct 04 2011
%E Extended by _T. D. Noe_, Oct 05 2011
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