1. Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral
- Creator:
- Talvila, Erik
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Taylor’s theorem, Henstock-Kurzweil integral, and Alexiewicz norm
- Language:
- English
- Description:
- When a real-valued function of one variable is approximated by its $n$th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock-Kurzweil integrable. When the only assumption is that $f^{(n)}~$ is Henstock-Kurzweil integrable then a modified form of the $n$th degree Taylor polynomial is used. When the only assumption is that $f^{(n)}\in C^0$ then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public