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.

## 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.

Item Type: | Article |
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Keywords: | Taylor's formula, Generalized Mean Value Theorem, Widder's Theorem, Nonparametric smoothing |

Full text: | Publisher-imposed embargo (VoR) Version of Record File format - PDF (73Kb) |

Status: | Peer-reviewed |

Publisher Web site: | http://www.maths.dur.ac.uk/~dma0je/Papers/einbeck_ijpam04.ps |

Record Created: | 11 May 2016 13:50 |

Last Modified: | 13 May 2016 10:16 |

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