  The aim of this note is to gather formal similarities between two apparently
different functions; {\em Euler's function} $\Gamma$ and {\em Anderson-Thakur
function} $\omega$. We discuss these similarities in the framework of the {\em
generalized Carlitz's module}, a common structure which can be helpful in
framing the theories of both functions. We further analyze several noticeable
differences while investigating the {\em exponential functions} associated to
these structures.
