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A175617 Decimal expansion of product_{n>=2} (1-n^(-6)).

%I A175617 #14 Feb 16 2025 08:33:12
%S A175617 9,8,2,6,8,4,2,7,7,7,4,2,1,9,2,5,1,8,3,2,4,4,7,5,9,1,6,2,5,7,1,3,6,3,
%T A175617 7,3,5,1,4,8,2,8,9,9,8,4,4,9,1,9,5,5,5,1,7,9,1,6,9,3,3,9,6,5,4,4,3,7,
%U A175617 8,7,1,0,9,0,0,3,7,0,0,8,6,2,3,6,1,8,4,8,6,6,9,9,8,0,0,7,8,4,7,5,6,1,5,7,6
%N A175617 Decimal expansion of product_{n>=2} (1-n^(-6)).
%H A175617 E. Weisstein, <a href="https://mathworld.wolfram.com/InfiniteProduct.html">Infinite Product</a>, Mathworld.
%F A175617 Equals product_{t=1..5} 1/Gamma(2-exp(Pi*i*t/3)), where i is the imaginary unit and Pi/3 = A019670.
%F A175617 Equals exp(Sum_{j>=1} (1 - zeta(6*j))/j). - _Vaclav Kotesovec_, Apr 27 2020
%e A175617 0.9826842777...
%p A175617 cosh(Pi*sqrt(3)/2)^2/6/Pi^2 ; evalf(%) ;
%t A175617 RealDigits[(1 + Cosh[Sqrt[3]*Pi])/(12*Pi^2), 10, 105] // First (* _Jean-François Alcover_, Feb 12 2013 *)
%o A175617 (PARI) exp(suminf(j=1, (1 - zeta(6*j))/j)) \\ _Vaclav Kotesovec_, Apr 27 2020
%Y A175617 Cf. A109219, A175615, A175619, A144665, A258871.
%K A175617 cons,easy,nonn
%O A175617 0,1
%A A175617 _R. J. Mathar_, Jul 26 2010