  Decimal expansions of classical constants such as $\sqrt2$, $\pi$ and
$\zeta(3)$ have long been a source of difficult questions. In the case of
Laurent series with coefficients in a finite field, where no carry-over
difficulties appear, the situation seems to be simplified and drastically
different. On the other hand, Carlitz introduced analogs of real numbers such
as $\pi$, $e$ or $\zeta(3)$. Hence, it became reasonable to enquire how
"complex" the Laurent representation of these "numbers" is. In this paper we
prove that the inverse of Carlitz's analog of $\pi$, $\Pi_q$, has in general a
linear complexity, except in the case $q=2$, when the complexity is quadratic.
In particular, this implies the transcendence of $\Pi_2$ over $\F_2(T)$. In the
second part, we consider the classes of Laurent series of at most polynomial
complexity and of zero entropy. We show that these satisfy some nice closure
properties.
