Lagrange’s essay “Recherches sur la manière de former des tables des planètes d’après les seules observations”

Massimo Galuzzi

Revue d'histoire des mathématiques (1995)

  • Volume: 1, Issue: 2, page 201-233
  • ISSN: 1262-022X

Abstract

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The memoir presented by Lagrange, which this paper examines, is usually considered as an elegant, but scarcely practicable, contribution to numerical analysis. The purpose of this study is to show the significance of the novel mathematical ideas it contains, and in particular to look at this essay from the perspective of generating function theory, for which the theoretical foundations would be laid some little time later by Laplace. This excursus of Lagrange’s does indeed proffer an abundance of procedures that were to become standard in this latter theory.Further, Lagrange’s memoir introduces some quite extraordinary elements, e.g. an algorithm for the approximation of an integral series by means of rational fractions — quite analogous in some cases to the determination of Padé approximants; or the introduction of polynomials formally akin to Chebyshev polynomials, to cater for tasks that would only devolve to the latter in the 20th century.

How to cite

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Galuzzi, Massimo. "Lagrange’s essay “Recherches sur la manière de former des tables des planètes d’après les seules observations”." Revue d'histoire des mathématiques 1.2 (1995): 201-233. <http://eudml.org/doc/252089>.

@article{Galuzzi1995,
abstract = {The memoir presented by Lagrange, which this paper examines, is usually considered as an elegant, but scarcely practicable, contribution to numerical analysis. The purpose of this study is to show the significance of the novel mathematical ideas it contains, and in particular to look at this essay from the perspective of generating function theory, for which the theoretical foundations would be laid some little time later by Laplace. This excursus of Lagrange’s does indeed proffer an abundance of procedures that were to become standard in this latter theory.Further, Lagrange’s memoir introduces some quite extraordinary elements, e.g. an algorithm for the approximation of an integral series by means of rational fractions — quite analogous in some cases to the determination of Padé approximants; or the introduction of polynomials formally akin to Chebyshev polynomials, to cater for tasks that would only devolve to the latter in the 20th century.},
author = {Galuzzi, Massimo},
journal = {Revue d'histoire des mathématiques},
keywords = {generating functions},
language = {eng},
number = {2},
pages = {201-233},
publisher = {Société mathématique de France},
title = {Lagrange’s essay “Recherches sur la manière de former des tables des planètes d’après les seules observations”},
url = {http://eudml.org/doc/252089},
volume = {1},
year = {1995},
}

TY - JOUR
AU - Galuzzi, Massimo
TI - Lagrange’s essay “Recherches sur la manière de former des tables des planètes d’après les seules observations”
JO - Revue d'histoire des mathématiques
PY - 1995
PB - Société mathématique de France
VL - 1
IS - 2
SP - 201
EP - 233
AB - The memoir presented by Lagrange, which this paper examines, is usually considered as an elegant, but scarcely practicable, contribution to numerical analysis. The purpose of this study is to show the significance of the novel mathematical ideas it contains, and in particular to look at this essay from the perspective of generating function theory, for which the theoretical foundations would be laid some little time later by Laplace. This excursus of Lagrange’s does indeed proffer an abundance of procedures that were to become standard in this latter theory.Further, Lagrange’s memoir introduces some quite extraordinary elements, e.g. an algorithm for the approximation of an integral series by means of rational fractions — quite analogous in some cases to the determination of Padé approximants; or the introduction of polynomials formally akin to Chebyshev polynomials, to cater for tasks that would only devolve to the latter in the 20th century.
LA - eng
KW - generating functions
UR - http://eudml.org/doc/252089
ER -

References

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