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A102887 Decimal expansion of Integral_{x=0..1} log(gamma(x))^2 dx.

%I A102887 #32 Sep 23 2022 16:27:00
%S A102887 1,8,6,6,3,1,7,0,8,3,7,9,3,5,6,2,0,8,0,9,9,2,9,6,7,9,3,7,9,7,8,2,8,9,
%T A102887 7,3,9,8,0,0,4,0,4,1,8,6,7,9,5,3,3,8,8,0,9,4,0,5,5,1,4,4,9,5,9,3,0,4,
%U A102887 0,9,6,5,9,8,4,9,0,5,6,3,0,3,4,7,5,5,2,3,9,8,6,0,2,9,2,5,7,2,5,0,8,5
%N A102887 Decimal expansion of Integral_{x=0..1} log(gamma(x))^2 dx.
%C A102887 Also equals (1/6)*log(2*Pi)^2 + 2*log(A)*log(2*Pi) - (1/6)*gamma*log(2*Pi) + Pi^2/48 + 2*gamma*log(A) + zeta''(2)/(2*Pi^2) (with A the Glaisher-Kinkelin constant). - _Jean-François Alcover_, Apr 29 2013
%D A102887 George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 236.
%H A102887 G. C. Greubel, <a href="/A102887/b102887.txt">Table of n, a(n) for n = 1..10000</a>
%H A102887 M. L. Glasser, <a href="https://doi.org/10.1080/00029890.2019.1565856">A note on Beukers's and related integrals</a>, Amer. Math. Monthly 126(4) (2019), 361-363.
%F A102887 Equals gamma^2/12 + Pi^2/48 + (gamma*log(2*Pi))/6 + log(2*Pi)^2/3 - ((gamma + log(2*Pi))*zeta'(2))/Pi^2 + zeta''(2)/(2*Pi^2).
%F A102887 Equals -Integral_{x=0..1, y=0..1} log(gamma(x*y))^2/log(x*y) dx dy. (Apply Theorem 1 or Theorem 2 in Glasser (2019).) - _Petros Hadjicostas_, Jun 30 2020
%e A102887 1.8663170837935620809929679379782897398...
%t A102887 EulerGamma^2/12 + Pi^2/48 + (EulerGamma*Log[2*Pi])/6 + Log[2*Pi]^2/3 - ((EulerGamma + Log[2*Pi])*Zeta'[2])/Pi^2 + Zeta''[2]/(2*Pi^2)
%o A102887 (PARI) intnum(x=0,1, log(gamma(x))^2) \\ _Michel Marcus_, Aug 27 2015
%Y A102887 Cf. A001620, A074962, A075700, A201994.
%K A102887 nonn,cons
%O A102887 1,2
%A A102887 _Eric W. Weisstein_, Jan 15 2005