- #1
- 13,348
- 3,108
Can "smooth" and "analytic" be used interchangeably?
My guess is 'yes'. :uhh:
Daniel.
My guess is 'yes'. :uhh:
Daniel.
No, smooth and analytic are not interchangeable. They have specific meanings in the scientific context and cannot be used interchangeably.
The main difference between smooth and analytic is that smooth refers to a function that has a continuous derivative, while analytic refers to a function that can be expressed as a power series.
Yes, a function can be both smooth and analytic. In fact, all analytic functions are also smooth, but not all smooth functions are analytic.
A common example of a smooth function is a polynomial, while a common example of an analytic function is the exponential function.
Yes, there is a relationship between smoothness and analyticity. As mentioned before, all analytic functions are smooth, but not all smooth functions are analytic. Additionally, smoothness is a necessary condition for analyticity.