A366174 Decimal expansion of a constant related to the asymptotics of A106336.

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

Offset

0,1

Links

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

Formula

Equals limit_{n->oo} A106336(n) * n^(3/2) * A106335^n.

Example

0.4983347979336034226063592640285001644306942823305129020199685349834...

Mathematica

val = Sqrt[(s^2*(-1 + r^2*s^2)*Log[r^2*s^2]^2 * QPochhammer[-1, r*s]^2)/ (2*Pi*(-2*r^2*s^2*(-1 + r^2*s^2)*Log[r^2*s^2]^2* Derivative[0, 1][QPochhammer][-1, r*s]^2 + r*s*(-1 + r^2*s^2)*Log[r^2*s^2]*QPochhammer[-1, r*s]* ((Log[r^2*s^2] + 4*Log[1 - r^2*s^2] + 4*QPolyGamma[0, 1, r^2*s^2])* Derivative[0, 1][QPochhammer][-1, r*s] + r*s*Log[r^2*s^2] * Derivative[0, 2][QPochhammer][-1, r*s]) + 2*r^4*s^3*(-1 + r^2*s^2) * Log[r^2*s^2]^2*QPochhammer[-1, r*s]^3 * Derivative[0, 2][QPochhammer][r^2*s^2, r^2*s^2] + QPochhammer[-1, r*s]^2*(16*r^2*s^2*ArcTanh[1 - 2*r^2*s^2] + (-1 + r^2*s^2)*Log[r^2*s^2]^2 - 8*Log[1 - r^2*s^2] - 4*(-1 + r^2*s^2)* Log[1 - r^2*s^2]^2 - 8*(-1 + r^2*s^2)*(-1 + Log[1 - r^2*s^2])* QPolyGamma[0, 1, r^2*s^2] + (4 - 4*r^2*s^2)* QPolyGamma[0, 1, r^2*s^2]^2 + 4*(-1 + r^2*s^2)*(QPolyGamma[1, 1, r^2*s^2] - 2*r^2*s^2*Log[r^2*s^2]* Derivative[0, 0, 1][QPolyGamma][0, 1, r^2*s^2]))))] /. FindRoot[{2*s == QPochhammer[-1, r*s]*QPochhammer[r^2*s^2], (-2*Log[1 - r^2*s^2] - 2*QPolyGamma[0, 1, r^2*s^2])/ Log[r^2*s^2] + (r* s*(Derivative[0, 1][QPochhammer][-1, r*s] + r*QPochhammer[-1, r*s]^2* Derivative[0, 1][QPochhammer][r^2*s^2, r^2*s^2]))/ QPochhammer[-1, r*s] == 1}, {r, 1/3}, {s, 2}, WorkingPrecision -> 600]; RealDigits[Chop[val], 10, -Floor[Log[10, Abs[Im[val]]]] - 3][[1]] (* r = A106335, s = A106334 *)

Crossrefs

Cf. A106334, A106335, A106336.

Sequence in context: A280630 A215617 A328229 * A198548 A134902 A110992

Adjacent sequences: A366171 A366172 A366173 * A366175 A366176 A366177

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 03 2023

Status

approved