I've been messing around with generating functions, power series, and related series, and I've come across a simple method of using two "roots of unity filters" to calculate the Hadamard product. A professor at a local university has offered to comment on my ideas, but I'm still searching for more information on Hadamard products. I'd like to know the history of them if possible, and Wikipedia and searches haven't turned up much. I'm especially interested in direct calculations of the Hadamard product. I seem to have a method that works for all generating functions. So I'd like to know if this is public knowledge, or if there is a chance I've discovered something new.
Again, my method essentially uses two generating functions to generate a complete generating function that is the Hadamard product. Is this new?