On Sat, 24 Jun 2023 20:17:27 +0200, "Richard B. Kreckel" <kreckel@in.terlu.de> said:
RK> Dear Vitaly, Thanks for your excellent treatise on the subject! RK> On 6/24/23 19:28, Vitaly Magerya wrote: >> This is why 1/(Order(x^n)) is not Order(x^-n), it can be >> Order(x^(-n-1)), or lower. RK> Okay. What would be the correct code for Order_power(x,e), RK> then? What about non-integers? I may be missing something, but I do not believe there is a meaningful connection between orders of f(x) and 1/f(x) as big-O. For example, Order(x^k*sin(1/x))=Order(k) at x=0 but Order(x^{-1}/sin(1/x)) is not finite. -- Vladimir V. Kisil http://www1.maths.leeds.ac.uk/~kisilv/ Book: Geometry of Mobius Maps https://doi.org/10.1142/p835 Soft: Geometry of cycles http://moebinv.sourceforge.net/ Jupyter notebooks: https://github.com/vvkisil?tab=repositories