A366072 Decimal expansion of a constant related to the asymptotics of A307399.

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

Offset: 1

Author

Vaclav Kotesovec, Sep 28 2023

Keywords

• nonn
• cons

Examples

			5.84278321476352032847350429253643509033417800773284061845774243558820314...
		

Crossrefs

Cf. A307399, A307401, A192206.

Programs

Mathematica

val = r /. FindRoot[{1 + (Log[1 - r*s] + QPolyGamma[0, 1, r*s])/Log[r*s] == s + r*s*Derivative[0, 1][QPochhammer][r*s, r*s] / QPochhammer[r*s], (-4*r*s*ArcTanh[1 - 2*r*s] + s*(1 - r*s)*Log[r*s]^2 + 2*Log[1 - r*s]) / (-1 + r*s) - 2*QPolyGamma[0, 1, r*s] + ((1 - s)*Log[r*s] + Log[1 - r*s] + QPolyGamma[0, 1, r*s])^2 - QPolyGamma[1, 1, r*s] + 2*r*s*Log[r*s]*Derivative[0, 0, 1][QPolyGamma][0, 1, r*s] == (-1 + 1/s + Log[1 - r*s]/(s*Log[r*s]) + QPolyGamma[0, 1, r*s]/(s*Log[r*s]) + r^2*s*Derivative[0, 2][QPochhammer][r*s, r*s] / QPochhammer[r*s])*s* Log[r*s]^2}, {r, 1/6}, {s, 2}, WorkingPrecision -> 90]; N[1/Chop[val], -Floor[Log[10, Abs[Im[val]]]] - 3]

Formula

Equals limit n->infinity A307399(n)^(1/n).