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A373207 Decimal expansion of Product_{k>=1} f(2*k)^2/(f(2*k-1) * f(2*k+1)), where f(k) = k^(1/k).

%I A373207 #7 May 28 2024 05:28:52
%S A373207 1,3,7,6,7,6,6,7,3,9,0,7,4,8,8,8,2,2,6,1,2,7,1,6,5,9,4,8,2,5,0,4,1,6,
%T A373207 2,9,9,0,8,7,1,2,4,3,9,0,3,7,9,9,2,6,4,1,7,7,1,3,3,1,1,4,6,0,8,1,8,7,
%U A373207 8,4,8,4,2,6,3,7,1,7,0,5,2,1,9,1,7,8,2,1,0,0,4,1,8,1,9,1,3,2,4,1,0,9,4,3,5
%N A373207 Decimal expansion of Product_{k>=1} f(2*k)^2/(f(2*k-1) * f(2*k+1)), where f(k) = k^(1/k).
%H A373207 Dirk Huylebrouck, <a href="https://doi.org/10.4169/amer.math.monthly.122.04.371">Generalizing Wallis' formula</a>, The American Mathematical Monthly, Vol. 122, No. 4 (2015), pp. 371-372; <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.122.04.371">alternative link</a>; <a href="https://arxiv.org/abs/1402.6577">arXiv preprint</a>, arXiv:1402.6577 [math.HO], 2014.
%H A373207 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>.
%H A373207 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet eta function</a>.
%F A373207 Equals exp(2*eta'(1)) = exp(2*A091812), where eta is the Dirichlet eta function.
%F A373207 Equals 2^(2*gamma - log(2)), where gamma is Euler's constant (A001620).
%e A373207 (2^(1/2)/1^1) * (2^(1/2)/3^(1/3)) * (4^(1/4)/3^(1/3)) * (4^(1/4)/5^(1/5)) * ...
%e A373207 1.37676673907488822612716594825041629908712439037992...
%t A373207 RealDigits[2^(2*EulerGamma - Log[2]), 10, 120][[1]]
%o A373207 (PARI) 2^(2*Euler - log(2))
%Y A373207 Cf. A001620, A002162, A091812, A373208.
%K A373207 nonn,cons
%O A373207 1,2
%A A373207 _Amiram Eldar_, May 28 2024