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A376815
Decimal expansion of a constant related to the asymptotics of A376812.
2
4, 1, 8, 3, 6, 2, 3, 0, 8, 2, 3, 1, 5, 0, 1, 0, 3, 7, 5, 9, 2, 4, 3, 4, 2, 0, 7, 4, 7, 1, 4, 3, 6, 2, 8, 9, 8, 9, 5, 6, 3, 8, 6, 9, 7, 7, 0, 7, 0, 3, 5, 8, 8, 7, 8, 5, 7, 8, 3, 2, 7, 1, 0, 0, 2, 0, 9, 8, 1, 9, 5, 1, 5, 7, 2, 6, 9, 5, 0, 8, 1, 6, 9, 4, 1, 1, 4, 8, 1, 0, 4, 6, 8, 4, 1, 7, 7, 0, 4, 5, 4, 9, 5, 3, 2
OFFSET
1,1
FORMULA
Equals limit_{n->infinity} A376812(n)^(1/sqrt(n)).
Equals A376660^2. - Vaclav Kotesovec, Oct 06 2024
Equals exp(sqrt(3*log(r)^2 + 8*polylog(2, r^(1/2)) - 2*Pi^2/3)), where r = A088559 = 0.4655712318767680266567312252199... is the real root of the equation r*(1+r)^2 = 1. - Vaclav Kotesovec, Oct 07 2024
EXAMPLE
4.18362308231501037592434207471436289895638697707035887857832710...
MATHEMATICA
RealDigits[E^Sqrt[3*Log[r]^2 + 8*PolyLog[2, r^(1/2)] - 2*Pi^2/3] /. r -> (-2 + ((29 - 3*Sqrt[93])/2)^(1/3) + ((29 + 3*Sqrt[93])/2)^(1/3))/3, 10, 120][[1]] (* Vaclav Kotesovec, Oct 07 2024 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Oct 05 2024
STATUS
approved