The Hadamard factorization theorem confirms the existence of Hadamard products of entire functions. But is there a feasible computational technique to find the Hadamard product of a given entire function?
My question originates from an exercise on Stein's Complex Analysis asking me to find Hadamard products of $e^{z} - 1$ and $\cos\pi z$. I found a question here, and it seems that the answer uses the characteristics of the functions themselves to get a hadamard product, and the method is not general for all entire functions.