  The Luria-Delbr{\"u}ck experiment is a cornerstone of evolutionary theory,
demonstrating the randomness of mutations before selection. The distribution of
the number of mutants in this experiment has been the subject of intense
investigation during the last 70 years. Despite this considerable effort, most
of the results have been obtained under the assumption of constant growth rate,
which is far from the experimental condition. We derive here the properties of
this distribution for arbitrary growth function, for both the deterministic and
stochastic growth of the mutants. The derivation we propose uses the number of
wild type bacteria as the independent variable instead of time. The derivation
is surprisingly simple and versatile, allowing many generalizations to be taken
easily into account.
