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Decimal expansion of a constant related to the asymptotics of A376530.
1

%I #22 Oct 09 2024 14:26:56

%S 4,9,8,8,0,2,0,8,7,6,6,0,0,9,0,3,8,0,5,3,3,5,2,2,4,4,6,0,7,9,0,7,7,3,

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

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

%N Decimal expansion of a constant related to the asymptotics of A376530.

%F Equals limit_{n->infinity} A376530(n)^(1/sqrt(n)).

%F Equals exp(2*sqrt(log(r)^2 + 2*polylog(2, 1-r) - 2*polylog(2, 1-r^3)/3)), where r = A192918 = 0.54368901269207636157085597180174... is the real root of the equation r^2 * (1-r^3)^2 = (1-r)^2.

%e 4.988020876600903805335224460790773050832038156091687962387444991919...

%t RealDigits[E^(2*Sqrt[Log[r]^2 + 2*PolyLog[2, 1-r] - 2*PolyLog[2, 1-r^3]/3]) /. r -> (-1 - 2/(17 + 3*Sqrt[33])^(1/3) + (17 + 3*Sqrt[33])^(1/3))/3, 10, 120][[1]]

%Y Cf. A376530, A376621.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Oct 09 2024