Historical synopsis of the Taylor remainder

Lars Erik Persson, Humberto Rafeiro, Peter Wall

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalNote di Matematica
Issue number1
Publication statusPublished - 2017
Externally publishedYes


  • History of Taylor remainder
  • Lagrange remainder
  • Taylor formula
  • Taylor remainder

ASJC Scopus subject areas

  • General Mathematics


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