OFFSET
0,1
FORMULA
Equals 1*sin(1/1) * 2*sin(1/2) * 3*sin(1/3) * 4*sin(1/4) * 5*sin(1/5) * ...
From Amiram Eldar, Jul 30 2023: (Start)
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.
Equals exp(-Sum_{k>=1} zeta(2*k)^2/(k*Pi^(2*k))). (End)
EXAMPLE
0.75536338851857321406336498617047655...
MAPLE
evalf(Product(n*sin(1/n), n = 1..infinity), 120); # Vaclav Kotesovec, Jun 23 2021
PROG
(PARI)
\\ Set the precision at least twice than the
\\ number of desired correct decimal digits
default(realprecision, 200); \\ To get the first 100 digits right
exp(-sumpos(n=1, -log(n*sin(1/n))))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Michal Paulovic, Nov 17 2017
EXTENSIONS
Terms corrected by Jinyuan Wang, Jul 21 2020
STATUS
approved