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A303670 Decimal expansion of Product_{k>=1} Gamma(1 + 1/k^2).

%I A303670 #18 Mar 09 2019 08:38:07
%S A303670 7,3,3,0,2,4,9,4,3,3,8,5,8,3,0,1,6,9,1,0,9,4,5,9,9,2,8,8,4,7,8,0,9,9,
%T A303670 3,4,9,8,4,5,3,3,8,3,5,0,5,0,0,1,0,2,2,1,9,8,2,2,3,0,0,5,9,6,1,7,2,4,
%U A303670 1,6,2,7,2,0,2,0,5,9,0,9,6,0,2,2,2,1,5,2,0,0,3,9,5,6,8,9,2,2,9,2,7,2,6,1,2,1
%N A303670 Decimal expansion of Product_{k>=1} Gamma(1 + 1/k^2).
%F A303670 Equals Product_{k>=1} Gamma(1/k^2) / k^2.
%F A303670 Equals exp(-gamma*Pi^2/6 + Sum_{k>=2} (-1)^k*zeta(k)*zeta(2*k)/k), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Mar 09 2019
%F A303670 Equals exp(-gamma*Pi^2/6 + A306774).
%e A303670 0.73302494338583016910945992884780993498453383505001022198223...
%p A303670 Digits := 120: evalf(product(GAMMA(1+1/n^2), n = 1..infinity));
%p A303670 evalf(exp(-gamma*Pi^2/6 + Sum((-1)^k*Zeta(k)*Zeta(2*k)/k, k=2..infinity)), 121); # _Vaclav Kotesovec_, Mar 09 2019
%t A303670 RealDigits[NProduct[Gamma[1 + 1/n^2], {n, 1, Infinity}, WorkingPrecision -> 120, NProductFactors -> 1000], 10, 70][[1]]
%o A303670 (PARI) exp(-Euler*Pi^2/6 + sumalt(k=2, (-1)^k*zeta(k)*zeta(2*k)/k)) \\ _Vaclav Kotesovec_, Mar 09 2019
%Y A303670 Cf. A306769, A306774, A324590.
%K A303670 nonn,cons
%O A303670 0,1
%A A303670 _Vaclav Kotesovec_, Apr 28 2018