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A246687 Decimal expansion of integral_{0..infinity} x*log(x)*(1-eta(x)^2) dx, where the function 'eta' is a solution of the Painlevé III differential equation. 0

%I

%S 0,9,1,9,2,7,5,7,5,7,7,4,7,1,8,0,2,3,8,1,5,0,4,0,2,4,3,2,1,1,0,7,2,2,

%T 6,3,5,8,1,4,0,0,7,2,9,2,9,5,4,5,6,4,5,2,7,6,2,5,0,3,5,8,0,2,0,0,9,3,

%U 2,8,1,9,5,1,7,4,0,9,6,0,0,8,4,1,8,2,1,6,9,3,5,8,2,9,4,8,6,9,8,8,8,2,2,9,7

%N Decimal expansion of integral_{0..infinity} x*log(x)*(1-eta(x)^2) dx, where the function 'eta' is a solution of the Painlevé III differential equation.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 402.

%F 1/4 + (7/12)*log(2) - 3*log(A) where A is the Glaisher-Kinkelin constant.

%e -0.0919275757747180238150402432110722635814007292954564527625...

%t Join[{0}, RealDigits[1/4 + (7/12)*Log[2] - 3*Log[Glaisher], 10, 104] // First]

%Y Cf. A074962.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Sep 01 2014

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Last modified September 27 22:01 EDT 2022. Contains 357063 sequences. (Running on oeis4.)