Historical synopsis of the Taylor remainder

Lars Erik Persson; Humberto Rafeiro; Peter Wall

doi:10.1285/i15900932v37n1p1

Historical synopsis of the Taylor remainder

Lars Erik Persson, Humberto Rafeiro, Peter Wall

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Note di Matematica
Volume	37
Issue number	1
DOIs	https://doi.org/10.1285/i15900932v37n1p1
Publication status	Published - 2017
Externally published	Yes

Keywords

History of Taylor remainder
Lagrange remainder
Taylor formula
Taylor remainder

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1285/i15900932v37n1p1

Cite this

@article{261b37fcb7b74ac8b16454d207a819cc,

title = "Historical synopsis of the Taylor remainder",

abstract = "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, Schl{\"o}milch, Roche, Cox, Turquan, Bourget, Koenig, Darboux, Amigues, Teixeira, Peano, Blumenthal, Wolfe and Gon{\c c}alves. We end the paper with a new Taylor remainder which generalizes the well-known Lagrange remainder.",

keywords = "History of Taylor remainder, Lagrange remainder, Taylor formula, Taylor remainder",

author = "Persson, {Lars Erik} and Humberto Rafeiro and Peter Wall",

note = "Publisher Copyright: {\textcopyright} 2017 Universit{\`a} del Salento.",

year = "2017",

doi = "10.1285/i15900932v37n1p1",

language = "English",

volume = "37",

pages = "1--21",

journal = "Note di Matematica",

issn = "1123-2536",

publisher = "Pitagora Editrice",

number = "1",

}

TY - JOUR

T1 - Historical synopsis of the Taylor remainder

AU - Persson, Lars Erik

AU - Rafeiro, Humberto

AU - Wall, Peter

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - History of Taylor remainder

KW - Lagrange remainder

KW - Taylor formula

KW - Taylor remainder

UR - http://www.scopus.com/inward/record.url?scp=85039711338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039711338&partnerID=8YFLogxK

U2 - 10.1285/i15900932v37n1p1

DO - 10.1285/i15900932v37n1p1

M3 - Article

AN - SCOPUS:85039711338

SN - 1123-2536

VL - 37

SP - 1

EP - 21

JO - Note di Matematica

JF - Note di Matematica

IS - 1

ER -

Historical synopsis of the Taylor remainder

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this