A327279 Decimal expansion of a constant related to A008485 and A327215.

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

Offset: 0

Author

Vaclav Kotesovec, Aug 28 2019

Keywords

• nonn
• cons

Examples

			0.26801521271073331568695383828032867950066675724203942644590415846953909499267...
		

Crossrefs

Cf. A008485, A270915, A327215, A327280, A366022.

Programs

Mathematica

val = Sqrt[(1 - r*s)*(Log[r*s]^2/(2*Pi*(4*ArcTanh[1 - 2*r*s]*(r*s + (-1 + r*s)*Log[r*s]) - 2*(1 + (-1 + r*s)*ArcTanh[1 - 2*r*s])*Log[1 - r*s] + (-1 + r*s)*(2 + 3*Log[r*s] - 2*Log[1 - r*s]) * QPolyGamma[0, 1, r*s] + (1 - r*s)* QPolyGamma[0, 1, r*s]^2 + (-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[{QPochhammer[r*s] == 1/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, 2}, WorkingPrecision -> 1000]; RealDigits[Chop[val], 10, -Floor[Log[10, Abs[Im[val]]]] - 3][[1]] (* Vaclav Kotesovec, Oct 02 2023 *)

Formula

Equals limit_{n->infinity} A008485(n) * sqrt(n) / A270915^n.