%I #8 Feb 23 2013 14:44:58

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

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

%U 7,1,7,2,8,6,1,2,5,7,0,6,6,4,6,6,2,2,7,4,4,2,6,4,4,6,0,9,0,9,8,6,6,1,1,2,2

%N Decimal expansion of product_{n=2..infinity} (n^10-1)/(n^10+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.

%e 0.99801282617298278419003981450896856553...

%t f[k_] := Sin[(-1)^(k/10)*Pi]; RealDigits[Pi/(5*Sinh[Pi])*Product[f[k], {k, {2, 4, 6, 8}}]/ Product[f[k], {k, {1, 3, 7, 9}}] // Re, 10, 105] // First (* _Jean-François Alcover_, Feb 12 2013 *)

%Y Cf. A090986.

%K nonn,cons,easy

%O 0,1

%A _R. J. Mathar_, Feb 01 2009

%E More terms from _Jean-François Alcover_, Feb 12 2013