Let $K$ be a field. For $m>1$, elements in the ring of power series in $m$ variables over $K$, i.e., $K[[X_1, \cdots, X_m]]$ look like - $$ \displaystyle\sum_{(i_1, \cdots, i_m)\in (\mathbb N_{0})^m} a_{i_1, \cdots, i_m} X_1^{i_1} \cdots X_m^{i_m}$$ where $\mathbb N_0$ is the set of non-negative integers.

**Is there an explicit expression for elements in its quotient field, i.e., the field of meromorphic series in $m$ variables?**

Using the geometric series, we know that for $m=1$, the elements look like $\displaystyle\sum_{i \geq r} a_i X^i$ for some integer $r$.