A144665 Decimal expansion of product_{n=2..infinity} (n^6-1)/(n^6+1).

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

Offset

0,1

Links

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

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

E. W. Weisstein, Infinite Product, MathWorld.

Formula

c=(Pi/3)*(cosh(sqrt(3)*Pi)+1)/(sinh(Pi)*(cosh(Pi)-cos(sqrt(3)*Pi))).

Example

0.96590608576215921215...

Mathematica

RealDigits[ -((Pi*(1 + Cosh[Sqrt[3]*Pi])*Csch[Pi])/(3*(Cos[Sqrt[3]*Pi] - Cosh[Pi]))), 10, 105] // First (* Jean-François Alcover, Feb 11 2013 *)

Prog

(PARI) Pi*(cosh(sqrt(3)*Pi)+1)/sinh(Pi)/(cosh(Pi)-cos(sqrt(3)*Pi))/3 \\ - M. F. Hasler, Feb 23 2013

Crossrefs

Cf. A090986.

Sequence in context: A247040 A019942 A102047 * A019884 A103814 A245770

Adjacent sequences: A144662 A144663 A144664 * A144666 A144667 A144668

Keyword

nonn,cons

Author

R. J. Mathar, Feb 01 2009

Status

approved