Coefficients on the p-adic expansions

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So a p-adic expansion of a rational number was presented to me as an analogue of a Laurent-series expansion and defined as:
$$\sum\limits_{n=-{\infty}}^{\infty}a_np^n$$
Can you find the coefficients for these the same way you would for a Laurent series? I've not gotten to that part of this book, but it mentions calculus on the p-adics.
 
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I've also resolved this question. Derivatives aren't defined on the p-adic numbers. And there is no "formula" for finding the coefficients.
 

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