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%I #20 Sep 26 2023 08:16:03
%S 5,3,5,2,7,0,1,3,3,3,4,8,6,6,4,2,6,8,7,7,7,2,4,1,5,8,1,4,1,6,5,3,2,7,
%T 8,7,9,8,5,1,4,8,3,2,7,1,2,8,6,9,4,7,0,9,7,3,1,9,6,9,0,7,5,6,0,6,4,1,
%U 0,2,1,5,1,2,6,7,5,3,1,5,5,2,2,3,2,3,4,2,7,6,4,4,7,8,8,5,4,2,2,8,2,2,8,1,7
%N Decimal expansion of a constant related to the asymptotics of A008485.
%H Vaclav Kotesovec, <a href="/A270915/b270915.txt">Table of n, a(n) for n = 1..500</a>
%F Equals limit n->infinity A008485(n)^(1/n).
%e 5.352701333486642687772415814165327879851483271286947097319690756...
%t RealDigits[1/r /. FindRoot[{s == 1/QPochhammer[r*s], QPochhammer[r*s] + r*s*Derivative[0, 1][QPochhammer][r*s, r*s] == (Log[1 - r*s] + QPolyGamma[0, 1, r*s]) / (s*Log[r*s])}, {r, 1/5}, {s, 1}, WorkingPrecision -> 120], 10, 105][[1]] (* _Vaclav Kotesovec_, Sep 26 2023 *)
%Y Cf. A008485, A109084, A109085, A206228, A270914, A303070, A304625, A327279.
%K nonn,cons
%O 1,1
%A _Vaclav Kotesovec_, Mar 25 2016
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