Abstract
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 < ∞.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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
Online ISBN: 978-1-4757-3254-2
eBook Packages: Springer Book Archive