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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 645736, 5 pages
Research Article

Taylor's Expansion Revisited: A General Formula for the Remainder

Department of Algebra and Mathematical Analysis, University of Almería, Almería, 04120 Andalucía, Spain

Received 22 March 2012; Accepted 31 May 2012

Academic Editor: Harvinder S. Sidhu

Copyright © 2012 José Juan Rodríguez Cano and Enrique de Amo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give a new approach to Taylor's remainder formula, via a generalization of Cauchy's generalized mean value theorem, which allows us to include the well-known Schölomilch, Lebesgue, Cauchy, and the Euler classic types, as particular cases.