TY - JOUR
T1 - Historical synopsis of the Taylor remainder
AU - Persson, Lars Erik
AU - Rafeiro, Humberto
AU - Wall, Peter
N1 - Funding Information:
H.R. was partially supported by the research project \Study of boundedness of operators in generalized Morrey spaces", ID-PRJ: 6576 of the Faculty of Sciences of Pontificia Universidad Javeriana, Bogot?, Colombia. H.R. thanks Lulea University of Technology for financial support for research visit in January-February of 2016
Publisher Copyright:
© 2017 Università del Salento.
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 -