Canonical product
= Canonical product
{title2=$\prod_n E_{p_n}(z/a_n)$}
A canonical product builds a prescribed discrete zero set from <Weierstrass elementary factors>. Choose the orders $p_n$ so that the logarithms of tail factors converge uniformly on each compact subset. <Infinite product convergence from logarithmic tails> then gives an <entire function> with exactly those zeros, counted with the prescribed multiplicities. When $\sum_n|a_n|^{-1}<\infty$, factors of order zero suffice.