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%I #24 May 22 2023 02:45:22
%S 1,1,7,1,9,5,3,6,1,9,3,4,4,7,2,9,4,4,5,3,0,0,7,8,1,1,4,4,4,3,6,1,3,8,
%T 5,3,4,5,4,7,7,0,1,5,0,4,8,1,7,9,2,8,1,3,0,3,3,3,1,5,0,0,9,4,4,5,0,3,
%U 3,0,4,7,6,9,7,7,4,2,7,3,2,7,1,3,9,3,0,4,3,5,6,2,4,8,3,1,4,7,9
%N Decimal expansion of g(1)+g(2)-g(4)-g(5), where g(k) = Sum_{m>=0} (1/(6*m+k)^2).
%C By summing over g(1)-g(5) and g(2)-g(4) separately we obtain A214552 for the first difference and a quarter of A086724 for the second difference. - _R. J. Mathar_, Jul 20 2012
%C 2/3 times this constant equals A086724 [Bailey, Borwein and Crandall, 2006] - _R. J. Mathar_, Jul 20 2012
%D L. Fejes Tóth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.
%H David H. Bailey, Jonathan M. Borwein, and Richard E. Crandall, <a href="https://doi.org/10.1088/0305-4470/39/40/001">Integrals of the Ising class</a>, Journal of Physics A: Mathematical and General, Vol. 39, No. 40 (2006), 12271; <a href="https://www.osti.gov/servlets/purl/901224">alternative link</a>.
%F Equals -Integral_{x=0..1} log(x)/(x^2-x+1) dx. - _Jean-François Alcover_, Aug 29 2014
%F Equals Integral_{x>=0} x/(exp(x) + exp(-x) - 1) dx. - _Amiram Eldar_, May 22 2023
%e 1.1719536193447294453... = A214552 + A086724/4 = 1/1^2 +1/2^2 -1/4^2 -1/5^2 +1/7^2 +1/8^2 -1/10^2 -1/11^2 ++--....
%t g[k_] := PolyGamma[1, k/6]/36; RealDigits[g[1] + g[2] - g[4] - g[5], 10, 99] // First (* _Jean-François Alcover_, Feb 12 2013 *)
%Y Cf. A086723-A086731, A214552.
%K nonn,cons
%O 1,3
%A _N. J. A. Sloane_, Jul 31 2003
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