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

0,1

Links

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

Formula

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

Example

0.26801521271073331568695383828032867950066675724203942644590415846953909499267...

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 *)

Crossrefs

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

Sequence in context: A246120 A300659 A155003 * A021377 A261875 A084686

Adjacent sequences: A327276 A327277 A327278 * A327280 A327281 A327282

Keyword

nonn,cons

Author

Vaclav Kotesovec, Aug 28 2019

Status

approved