**Fields of power series **

• Power series expansions

By analogy with the decimal expansion for a real number, we introduce the following formal expression :

**X = a _{n}T^{n} + a_{n-1}T^{n-1}
+ a_{n-2}T^{n-2} +...... **

• Formal Integers

If the above expansion has only a finite number of terms, each one with a positive degree, we can write

**X = a _{n}T^{n} + a_{n-1}T^{n-1}
+ .......+ a_{m}T^{m}**

**X = (a _{n}T^{n-k} + a_{n-1}T^{n-k-1}
+ .......+ a_{k}) / T^{-k}**