If you look at the graph of sin (x) you see that all the zeroes are located at multiples of pi. So if you were to factor sin (x) as if it were a polynomial you would get m * x * (x-pi) * (x + pi) * ( x-2pi) * (x + 2pi) * ( x - 3pi ) * (x + 3pi) ..... (x - n pi) * ( x + n pi) as n approaches infinity. Question: what is m? I figured this much from computer experiments, m is not a constant, it is a function of x and n. m is less than 0 if n is odd, m is greater than 0 if n is even.
If you graph abs (x) and scaled it by the appropriate very large factor you'd see that m (x) looks like a bump centered at x =0 which morphs as n increases, it retains the bump figure. It is not of the form c * exp ( - k x2), although it looks like it could be.
What is this mystery function m? Please help me figure this out.