A366022 Decimal expansion of a constant related to the asymptotics of A109085.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Formula

Equals limit_{n->infinity} A109085(n) * n^(3/2) / A270915^n.

Example

0.489635226684303373081541660578468619322416625...

Mathematica

val = -s*Log[r*s] / Sqrt[2*Pi*((-2 - 3*Log[r*s] + 2*Log[1 - r*s])* QPolyGamma[0, 1, r*s] + QPolyGamma[0, 1, r*s]^2 - 4*ArcTanh[1 - 2*r*s]*(Log[r*s] - Log[1 - r*s]/2 - r*(s/(1 - r*s))) - 2*(Log[1 - r*s]/(1 - r*s)) - QPolyGamma[1, 1, r*s] + r*s*Log[r* s]*((-r)*s^2*Log[r*s]* Derivative[0, 2][QPochhammer][r*s, r*s] + 2*Derivative[0, 0, 1][QPolyGamma][0, 1, r*s]))] /. FindRoot[{s == 1/QPochhammer[r*s], 1/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 -> 1000]; RealDigits[Chop[val], 10, -Floor[Log[10, Abs[Im[val]]]] - 3][[1]]

Crossrefs

Cf. A109085, A270915, A366018.

Sequence in context: A328906 A194623 A373642 * A316251 A108616 A200634

Adjacent sequences: A366019 A366020 A366021 * A366023 A366024 A366025

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 26 2023

Status

approved