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

1,1

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

5.84278321476352032847350429253643509033417800773284061845774243558820314...

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]

Crossrefs

Cf. A307399, A307401, A192206.

Sequence in context: A212162 A249445 A199450 * A019649 A224833 A246926

Adjacent sequences: A366069 A366070 A366071 * A366073 A366074 A366075

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 28 2023

Status

approved