I just realized that the convolution of any function with itself many times will ultimately give a gaussian. I was just wondering if there was a function that was an exception to this?
What makes you think this? In raising a function to a very high power, the parts with |f(x)|>1 get increasingly larger while those with |f(x)|<1 vanish. So, for example, if the function has several narrow peaks whose height is greater than one, its very high powers will have spikes where each of those peaks were and vanish everywhere else.rasing any well defined function to a high integer power gives something increasingly similar to a Gaussian.