Re: a infinity product

[Johann Wiesenbauer]

> Find \prod_{i=1..inf} (1 + 1/i^2)
> 

Well, you could consider the function 

f(z) = exp(pi*z)-exp(-pi*z) 

and notice that it has exactly the (simple) zeros 
z = k*i, where k is any integer. Obviously, the same is true for the function 
g(z) defined by the convergent infinite product

g(z) = z * prod_{k=1..inf} (1 + z^2/k^2)

Following in Euler's footsteps, you might conclude from this that f(z) = C*g(z) 
for some real constant C, which can be obtained as the limit of f(z)/z, if z 
goes to 0. Take on from here to get the result already mentioned by others.

Johann