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

%I #11 Nov 18 2015 04:59:56

%S 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,

%T 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,

%U 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

%N Decimal expansion of product_{n=2..infinity} (n^9-1)/(n^9+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 0.99599126589340465511919...

%t 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 *)

%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 11 2013