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

%I #15 Jun 13 2015 06:42:17

%S 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,

%T 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,

%U 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

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

%H J. Borwein et al., <a href="http://www.ams.org/mathscinet-getitem?mr=2051473">Experimentation in Mathematics</a>, 2004, section 1.2.

%H E. W. Weisstein, <a href="http://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>, MathWorld.

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

%e 0.96590608576215921215...

%t 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 *)

%o (PARI) Pi*(cosh(sqrt(3)*Pi)+1)/sinh(Pi)/(cosh(Pi)-cos(sqrt(3)*Pi))/3 \\ - _M. F. Hasler_, Feb 23 2013

%Y Cf. A090986.

%K nonn,cons

%O 0,1

%A _R. J. Mathar_, Feb 01 2009