By a Paley-Wiener function I mean a function $f(z)$ that is the Fourier image of a test function. Equivalently, by Paley-Wiener theorem, $f(z)$ is an entire function that is of rapid decay on the real line and has a finite exponential type, $$ |f(z)|\le\frac{C_ne^{B|\mathrm{Im}z|}}{1+|\mathrm{Re}z|^n},\quad\forall n\in\mathbb{N}. $$

**Question:** What is the simplest explicit formula for a non-zero Paley-Wiener function?

The best I can think of right now is $$ f(z)=\int_0^1dte^{-\imath zt-\frac1{t(1-t)}} $$ which is not really explicit. Thanks.