Historical synopsis of the Taylor remainder

Authors

  • Lars-Erik Persson
  • Humberto Rafeiro
  • Peter Wall

DOI:

https://doi.org/10.1285/i15900932v37n1p1

Keywords:

Taylor formula, Taylor remainder, history of Taylor remainder, Lagrange remainder

Abstract

In this paper we give an historical synopsis of various Taylor remainders and their di erent proofs (without being exhaustive). We overview the formulas and the proofs given by such names as Bernoulli, Taylor, MacLaurin, Lagrange, Lacroix, Cauchy, Schlomilch, Roche Cox, Turquan, Bourget, Koenig, Darboux, Amigues, Teixeira, Peano, Blumenthal, Wolfe and Gon calves. We end the paper with a new Taylor remainder which generalizes the well-known Lagrange remainder.

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Published

28-11-2017

Issue

Volume 37, Issue 1 (2017)

Section

Articoli

License

Authors who publish with this publication accept all the terms and conditions of the Creative Commons license at the link below.

Gli autori che pubblicano in questa rivista accettano i termini e le condizioni specificate nella licenza Creative Commons di cui al link sottostante.

http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode