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Department of Mathematical Sciences

Academic Staff

Publication details for Jochen Einbeck

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): 69-74.

Author(s) from Durham

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.