Calculus in the p-adic domain is rather straightforward. Let us emphasize, however, that:
A function with a continuous derivative is not necessarily strictly differentiable.
The mean value theorem is valid provided the increment is small enough: |h| ≤ r p .
The radius of convergence of the exponential series is r p < ∞.
KeywordsPower Series Unit Ball Formal Power Series Residue Field Bernoulli Polynomial
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