Weierstrass product

Summary

A Weierstrass product is an infinite product of elementary factors $E_{p_n}(z/a_n)$ that converges to an entire function with zeros exactly at the points $a_n$. Each elementary factor is $1 - z/a_n$ times an exponential correction that makes the product converge. Weierstrass products show that any sequence of nonzero complex numbers tending to infinity is the zero set of an entire function. They are the building blocks of the Weierstrass factorization theorem and the Hadamard factorization theorem.