13 Jan
2012
13 Jan
'12
3:54 p.m.
Consider the infinite product:
(24/16) * (48/64) * (120/144) * ... * ((p^2 - 1)/(16*[p/4]^2)) * ...
In Sloane notation, this is:
Product (n >= 1) of (A061066(n+1) / (2*A024698(n+1)^2))
I've just realised that it has a much simpler representation: Product (p >= 5) of: (p+1)/(p-1) iff p = 4k + 1 (p-1)/(p+1) iff p = 4k - 1 = (6/4 . 6/8 . 10/12 . 14/12 . 18/16 . 18/20 . 22/24 . ...) = 1. Sincerely, Adam P. Goucher