Professor Jochen Einbeck jochen.einbeck@durham.ac.uk
Professor
A Simple Unifying Formula for Taylor's Theorem and Cauchy's Mean Value Theorem
Einbeck, Jochen
Authors
Abstract
We introduce a formula which generalizes Taylor's theorem from powers of linear terms z-x to functional terms \phi(z)-\phi(x), leading to a formula which reduces in a special case to Cauchy's generalized mean value theorem. In other words, regarding Cauchy's mean value theorem as an extension of the simple mean value theorem, we provide the analogous extension of Taylor's theorem. The filling of this gap is easy and requires only mathematics on an undergraduate level, so that the mentioned analogy might be a useful tool for illustration at schools and universities.
Citation
Einbeck, J. (2004). A Simple Unifying Formula for Taylor's Theorem and Cauchy's Mean Value Theorem. International Journal of Pure and Applied Mathematics, 14(1), 69-74
Journal Article Type | Article |
---|---|
Publication Date | Apr 1, 2004 |
Deposit Date | May 11, 2016 |
Publicly Available Date | Mar 28, 2024 |
Journal | International journal of pure and applied mathematics : IJPAM. |
Print ISSN | 1311-8080 |
Electronic ISSN | 1314-3395 |
Publisher | Academic Publications |
Peer Reviewed | Peer Reviewed |
Volume | 14 |
Issue | 1 |
Pages | 69-74 |
Keywords | Taylor's formula, Generalized Mean Value Theorem, Widder's Theorem, Nonparametric smoothing. |
Publisher URL | https://ijpam.eu/contents/2004-14-1/8/index.html |
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