A270914 - OEIS

%I #18 Sep 26 2023 07:08:47

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

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

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

%N Decimal expansion of a constant related to the asymptotics of A270913.

%C This constant is very close to exp(5*Pi/(6*sqrt(2))) / sqrt(2) = 4.502476748630924546525119125234175537729... - _Vaclav Kotesovec_, May 17 2018

%F Equals limit n->infinity A270913(n)^(1/n).

%e 4.502476747617354487738593932700784406763128756091621633464540424...

%t RealDigits[1/r /. FindRoot[{2*s == QPochhammer[-1, r*s], r*Derivative[0, 1][QPochhammer][-1, r*s] == 2}, {r, 1/2}, {s, 1/2}, WorkingPrecision -> 120], 10, 105][[1]] (* _Vaclav Kotesovec_, Sep 26 2023 *)

%Y Cf. A181315, A206229, A270913, A270915, A303071, A304626, A327280.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Mar 25 2016