Abstract
Calculus in the p-adic domain is rather straightforward. Let us emphasize, however, that:
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A function with a continuous derivative is not necessarily strictly differentiable.
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The mean value theorem is valid provided the increment is small enough: |h| ≤ r p .
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The radius of convergence of the exponential series is r p < ∞.
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© 2000 Springer Science+Business Media New York
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Robert, A.M. (2000). Differentiation. In: A Course in p-adic Analysis. Graduate Texts in Mathematics, vol 198. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3254-2_5
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DOI: https://doi.org/10.1007/978-1-4757-3254-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3150-4
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