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"Principe du maximum, inégalité de Harnack et unicité du probleme de Cauchy pour les opérateurs elliptiques dégénérés." In Annales de l'Institut Fourier, vol. 19, no. 1, pp. 277–304. 1969. with Pierre Schapira : "Propagation des singularités analytiques pour les solutions des équations aux dérivées partielles."
While Rolle's forte was always Diophantine analysis, his most important work was a book on the algebra of equations, called Traité d'algèbre, published in 1690. In that book Rolle firmly established the notation for the n th root of a real number, and proved a polynomial version of the theorem that today bears his name.
In which case the equation can be derived using perturbation theory. In 1770, Joseph Louis Lagrange (1736–1813) published his power series solution of the implicit equation for v mentioned above. However, his solution used cumbersome series expansions of logarithms.
Legendre introduced a three-fold classification –three kinds– which was a crucial simplification of the rather complicated theory at that time. Other important works of Legendre are: Mémoire sur les transcendantes elliptiques (1792), [16] Exercices de calcul intégral (1811–1817), [17] Traité des fonctions elliptiques (1825–1832). [18]
Suppose z is defined as a function of w by an equation of the form = where f is analytic at a point a and ′ Then it is possible to invert or solve the equation for w, expressing it in the form = given by a power series [1]
All second order differential equations with constant coefficients can be transformed into their respective canonic forms. This equation is one of these three cases: Elliptic partial differential equation, Parabolic partial differential equation and Hyperbolic partial differential equation.
Memoires in Histoire de l'Académie Royale des Sciences. 1783 Sur l'attraction des Sphéroïdes homogènes (work on Legendre polynomials) 1784 Recherches sur la figure des Planètes p. 370; 1785 Recherches d'analyse indéterminée p. 465 (work on number theory) 1786 Mémoire sur la manière de distinguer les Maxima des Minima dans le Calcul des ...
Méthode de concentration-compacité en calcul des variations Guy Henniart: Sur les conjectures de Langlands: 1983–1984 Laurent Clozel: Changement de base pour les formes automorphes sur le groupe linéaire 1984–1985 Joseph Oesterlé: Démonstration de la conjecture de Bieberbach d’après Louis de Branges: 1985–1986 Jean-Pierre Demailly