3 ms·
> That's not exactly true. For example, arctan = tan^-1 is smooth on R, but its Taylor series only converges for |x|<=1. This issue creeps in a lot but I think
by ithinkso 4y ago
> That's not exactly true. For example, arctan = tan^-1 is smooth on R, but its Taylor series only converges for |x|<=1.
This issue creeps in a lot but I think it comes from the complex analysis, where differentiable function is always smooth and analytic (holomorphic).
- bmitc 4y agoBut as far as I know, there is no corresponding dual analysis. The dual numbers do not form a field. The issue primarily revolves around elementary functions, compositions of them, and polynomials.
- ithinkso 4y agoYeah, I was only trying to explain where the issue (assuming smooth=analytic, that you rightfully pointed out) might have come from