On the identification of Wiener-Hopf factors

This note is concerned with the identification of the Wiener-Hopf factors of a function $1-f$, where $f$ generates an aperiodic distribution on the integers with a negative mean. The general and rational cases are addressed. We give a concise summary of the main practical facts needed for calculations involving the Wiener-Hopf factors. The basic facts are cited from the literature, but a few aspects are briefly proven here.