Oeuvres complètes de Niels Henrik Abel: Nouvelle édition

Niels Henrik Abel

doi:10.1017/CBO9781139245807

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 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', which states that the general fifth-degree polynomial is unsolvable by algebraic means. Also included in this volume is Abel's 'Paris memoir', which contains his many fundamental results on transcendental functions - in particular on elliptic integrals, elliptic functions, and what are known today as abelian integrals.

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Contents

Frontmatter
pp i-i
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PREFACE
pp ii-vii
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TABLE DES MATIÈRES DU TOME PREMIER
pp viii-ix
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I - Méthode générale pour trouver des fonctions d'une seule quantité variable, lorsqu'une propriété de ces fonctions est exprimée par une équation entre deux variables
pp 1-10
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II - Solution de quelques problèmes à l'aide d'intégrales définies
pp 11-27
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III - Mémoire sur les equations algébriques, où l'on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré
pp 28-33
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IV - L'intégrale finie ≤nɸx exprimée par une intégrale définie simple
pp 34-39
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V - Petite contribution à la théorie de quelques fonctions transcendantes
pp 40-60
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VI - Recherche des fonctions de deux quantités variables indépendantes x et y, telles que f(x,y), qui ont la propriété que f(z,f(x,y)) est une fonction symétrique de z, x et y
pp 61-65
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VII - Démonstration de l'impossibilité de la résolution algébrique des équations générales qui passent le quatrième degré
pp 66-94
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VIII - Remarque sur le mémoire No 4 du premier cahier du Journal de M. Crelle
pp 95-96
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IX - Résolution d'un problème de mécanique
pp 97-101
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X - Démonstration d'une expression de laquelle la formule binôme est un cas particulier
pp 102-103
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XI - Sur l'intégration de la formule différentielle ƍdx/R et ƍ étant des fonctions entières
pp 104-144
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XII - Mémoire sur une propriété générale d'une classe très étendue de fonctions transcendantes
pp 145-211
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XIII - Recherche de la quantité qui satisfait à la fois à deux éqùations algébriques données
pp 212-218
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XIV - Recherches sur la série 1 + m/1x + m(m-1/1.2)x2 +
pp 219-250
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XV - Sur quelques intégrales définies
pp 251-262
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XVI - Recherches sur les fonctions elliptiques
pp 263-388
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XVII - Sur les fonctions qui satisfont à l'équation ɸx + ɸy = Ψ(xfy + yfx)
pp 389-398
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XVIII - Note sur un mémoire de M. L. Olivier, ayant pour titre “Remarques sur les séries infinies et leur convergence”
pp 399-402
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XIX - Solution d'un problème général concernant la transformation des fonctions elliptiques
pp 403-428
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XX - Addition au mémoire précédent
pp 429-443
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XXI - Remarques sur quelques propriétés générales d'une certaine sorte de fonctions transcendantes
pp 444-456
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XXII - Sur le nombre des transformations différentes qu'on peut faire subir à une fonction elliptique par la substitution d'une fonction rationnelle dont le degré est un nombre premier donné
pp 457-465
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XXIII - Théorème général sur la transformation des fonctions elliptiques de la seconde et de la troisième espèce
pp 466-466
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XXIV - Note sur quelques formules elliptiques
pp 467-477
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XXV - Mémoire sur une classe particulière d'équations résolubles algébriquement
pp 478-507
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XXVI - Théorèmes sur les fonctions elliptiques
pp 508-514
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XXVII - Démonstration d'une propriété générale d'une certaine classe de fonctions transcendantes
pp 515-517
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Oeuvres complètes de Niels Henrik Abel

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