A144668 Decimal expansion of Product_{n=2..infinity} (n^9-1)/(n^9+1).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

J. Borwein et al., Experimentation in Mathematics, 2004, section 1.2.

Ryan Goulden, Closed-Form Evaluation of Arctanh Power Sums via Infinite Products, arXiv preprint arXiv:2602.06244 [math.GM], 2026.

E. W. Weisstein, Infinite Product, MathWorld.

Formula

Equals exp(-2*Sum_{k>=2} arctanh(1/k^9)). - Detlef Meya, Mar 25 2026

Example

0.99599126589340465511919...

Mathematica

p = 2/3*Product[Gamma[2 + (-1)^(k + k/9)], {k, {1, 2, 4, 5, 7, 8}}]/ Product[Gamma[2 - (-1)^(k + k/9)], {k, {1, 2, 4, 5, 7, 8}}]; RealDigits[Re[p], 10, 105][[1]] (* Jean-François Alcover, Feb 11 2013, updated Nov 18 2015 *)

Crossrefs

Cf. A090986, A144664, A144666.

Sequence in context: A175619 A342683 A136130 * A340222 A021505 A346930

Adjacent sequences: A144665 A144666 A144667 * A144669 A144670 A144671

Keyword

nonn,cons,easy

Author

R. J. Mathar, Feb 01 2009

Extensions

More terms from Jean-François Alcover, Feb 11 2013

Status

approved