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A simple unifying formula for Taylor's Theorem and Cauchy's Mean Value Theorem.

Einbeck, Jochen (2004) 'A simple unifying formula for Taylor's Theorem and Cauchy's Mean Value Theorem.', International journal of pure and applied mathematics., 14 (1). pp. 69-74.


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.

Item Type:Article
Keywords:Taylor's formula, Generalized Mean Value Theorem, Widder's Theorem, Nonparametric smoothing.
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Record Created:11 May 2016 13:50
Last Modified:16 Nov 2017 14:48

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