Definition:P-adic Expansion

Definition
Let $p$ be a prime number.

A $p$-adic expansion is a series in the rational numbers $\Q$ of the form:
 * $\displaystyle \sum_{n \mathop = m}^\infty \dfrac {d_n} {p^{-n}}$

where:
 * $\quad m \in \Z_{\le 0}$
 * $\quad \forall n \in \Z_{\ge m}: d_n \in \N \mathop {\text{ and } } 0 \le d_n < p$
 * $\quad m < 0 \implies d_m \neq 0$