Can you give any examples? How does this relate to the Taylor series? Is it trye that all analytic functions are smooth, but not all smooth functions are analytic?
2026-04-09 15:40:07.1775749207
What do people mean by a "smooth but not analytic" function?
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This has been asked and answered before. Here's the link: What is the difference between the terms smooth, analytical and continuous?
But anyway, smooth functions are infinitely differentiable. That is, all of their higher order derivates exist.
A function is analytic at a point if it has a power series expansion that converges in some disk about this point.
Analytic functions are also smooth functuins, but the converse is not true.
Below is a link to an example of a function that is smooth but not analytic: https://en.m.wikipedia.org/wiki/Non-analytic_smooth_function