cp's OEIS Frontend

A295219 Decimal expansion of Product_{n>=1} n*sin(1/n).

%I A295219 #29 Jul 30 2023 02:25:44
%S A295219 7,5,5,3,6,3,3,8,8,5,1,8,5,7,3,2,1,4,0,6,3,3,6,4,9,8,6,1,7,0,4,7,6,5,
%T A295219 5,3,5,9,6,1,2,9,6,3,6,7,9,2,1,3,0,1,4,2,5,5,7,0,2,2,5,0,4,3,3,3,6,2,
%U A295219 5,9,4,1,6,7,5,7,8,9,5,9,4,0,9,5,8,0,1,5
%N A295219 Decimal expansion of Product_{n>=1} n*sin(1/n).
%F A295219 Equals 1*sin(1/1) * 2*sin(1/2) * 3*sin(1/3) * 4*sin(1/4) * 5*sin(1/5) * ...
%F A295219 From _Amiram Eldar_, Jul 30 2023: (Start)
%F A295219 Equals exp(Sum_{k>=1} 2^(2*k-1)*(-1)^k*B(2*k)*zeta(2*k)/(k*(2*k)!)), where B(k) is the k-th Bernoulli number.
%F A295219 Equals exp(-Sum_{k>=1} zeta(2*k)^2/(k*Pi^(2*k))). (End)
%e A295219 0.75536338851857321406336498617047655...
%p A295219 evalf(Product(n*sin(1/n), n = 1..infinity), 120); # _Vaclav Kotesovec_, Jun 23 2021
%o A295219 (PARI)
%o A295219   \\ Set the precision at least twice than the
%o A295219   \\ number of desired correct decimal digits
%o A295219   default(realprecision, 200);  \\ To get the first 100 digits right
%o A295219   exp(-sumpos(n=1, -log(n*sin(1/n))))
%Y A295219 Cf. A118817.
%Y A295219 Cf. A027641, A027642.
%K A295219 nonn,cons
%O A295219 0,1
%A A295219 _Michal Paulovic_, Nov 17 2017
%E A295219 Terms corrected by _Jinyuan Wang_, Jul 21 2020