It is well known that if the ${eta}$-expansion of any nonnegative integer is finite, then ${eta}$ is a Pisot or Salem number. We prove here that $mathbb{F}_q((x^{-1}))$, the ${eta}$-expansion of the polynomial part of ${eta}$ is finite if and only if ${eta}$ is a Pisot series. Consequently we give an other proof of Scheiche theorem about finiteness property in $mathbb{F}_q((x^{-1}))$. Finally we show that if the base ${eta}$ is a Pisot series, then there is a bound of the length of the fractional part of ${eta}$-expansion of any polynomial P in $mathbb{F}_q[x]$.