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:
 * $\displaystyle \sum_{n \mathop = m}^\infty d_n p^n$

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

Also see

 * Every P-adic Expansion is a Cauchy Sequence in P-adic Norm


 * Every P-adic Expansion Converges to P-adic Number