Oeuvres complètes de Niels Henrik Abel: Nouvelle édition

Niels Henrik Abel

doi:10.1017/CBO9781139245814

Oeuvres complètes de Niels Henrik Abel

Nouvelle édition

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Valério, Duarte Machado, José Tenreiro and Kiryakova, Virginia 2014. Some pioneers of the applications of fractional calculus. Fractional Calculus and Applied Analysis, Vol. 17, Issue. 2, p. 552.

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Dagsvik, John K. 2021. Handbook of the History and Philosophy of Mathematical Practice. p. 1.

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MARTÍNEZ-JIMÉNEZ, Leonardo LÓPEZ-LARA, Pedro FLORES-BALDERAS, Adán and LÓPEZ-HERNÁNDEZ, Juan Manuel 2022. Automatic blood vessel detection using fractional Hessian matrices. ECORFAN Journal Taiwan, p. 12.

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Volume 2
Niels Henrik Abel
Edited by L. Sylow, S. Lie

Publisher:: Cambridge University Press
Online publication date:: August 2013
Print publication year:: 2012
First published in:: 1881
Online ISBN:: 9781139245814
DOI:: https://doi.org/10.1017/CBO9781139245814

Subjects:: Mathematics (general), Mathematics, History of Mathematical Texts, Algebra
Series:: Cambridge Library Collection - Mathematics

34.99 (GBP)

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Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 2 contains additional articles on elliptic functions and infinite series. It also includes extracts from Abel's letters, as well as detailed notes and commentary by Sylow and Lie on Abel's pioneering work.

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Oeuvres complètes de Niels Henrik Abel

Nouvelle édition

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Frontmatter
pp i-iv

CONTENTS
pp v-vi

I - Les fonctions transcendantes [equation not displayed] exprimées par des intégrales définies
pp 1-6

II - Sur l'intégrale définie [equation not displayed]
pp 7-13

III - Sommation de la série y = φ(0) + φ(1) x + φ(2) x2 + φ(3) x3 + ... + φ(n) xnn étant un nombre entier positif fini ou infini, et φ(n) une fonction algébrique rationnelle de n
pp 14-18

IV - Sur l'équation différentielle dy + (p + qy + ry2)dx = 0, où p, q et r sont des fonctions de x seul
pp 19-25

V - Sur l'équation différentielle (y +s) dy + (p + qy + ry2) dx = 0
pp 26-35

VI - Détermination d'une fonction au moyen d'une équation qui ne contient qu'une seule variable
pp 36-39

VII - Propriétés remarquables de la fonction y = φx déterminée par l'équation [equation not displayed] étant une fonction quelconque de yqui ne devient pas nulle ou infinie lorsque y = a, a1, a2, ... am
pp 40-42

VIII - Sur une propriété remarquable d'une classe très étendue de fonctions transcendantes
pp 43-46

IX - Extension de la théorie précédente
pp 47-54

X - Sur la comparaison des fonctions transcendantes
pp 55-66

XI - Sur les fonctions génératrices et leurs déterminantes
pp 67-81

XII - Sur quelques intégrales définies
pp 82-86

XIII - Théorie des transcendantes elliptiques
pp 87-188

XIV - Note sur la fonction [equation not displayed]
pp 189-193

XV - Démonstration de quelques formules elliptiques
pp 194-196

XVI - Sur les séries
pp 197-205

XVII - Mémoire sur les fonctions transcendantes la ʃy dx où y est une fonction algébrique de x
pp 206-216

XVIII - Sur la résolution algébrique des équations
pp 217-243

XIX - Fragmens sur les fonctions elliptiques
pp 244-253

XX - Extraits de quelques lettres à Holmboe
pp 254-262

XXI - Extrait d'une lettre à Hansteen
pp 263-265

XXII - Extraits de quelques lettres à Crelle
pp 266-270

XXIII - Lettre à Legendre
pp 271-280

NOTES
pp 281-338

Table pour faciliter la recherche des citations
pp 339-340

ERRATA
pp 341-341

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Oeuvres complètes de Niels Henrik Abel

Nouvelle édition

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