Entire function of exponential type ($|f(z)|\le A{e}^{B|z|}$)

An entire function is of exponential type if constants $A,B>0$ give the displayed bound everywhere. A genus-zero canonical product with ${\sum }_n|a_n{|}^{-1}<\infty$ obeys $|{\prod }_n(1-z/a_n)|\le \exp (|z|{\sum }_n|a_n{|}^{-1})$, since $1+u\le e^u$ for $u\ge 0$.