1. Sur deux formules de Frobenius et Stickelberger et inversion de Lagrange
- Author
-
Roger Gay, Marcel Grangé, Ahmed Sebbar, Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Pure mathematics ,Mathematics::General Mathematics ,[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] ,[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] ,01 natural sciences ,Inversion (discrete mathematics) ,Bell polynomials ,symbols.namesake ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,0101 mathematics ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,Applied Mathematics ,010102 general mathematics ,[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] ,Extension (predicate logic) ,Operator theory ,010101 applied mathematics ,Algebra ,Computational Mathematics ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,Computational Theory and Mathematics ,Mathematics - Classical Analysis and ODEs ,Lagrange inversion theorem ,symbols - Abstract
We give a proof and extension of two formulas of Frobenius and Stickelberger of Differential Calculus that they used in a fundamental paper concerning elliptic functions theory. Our main ingredient is the introduction of a bilinear form which is a vast generalization of Leibniz formula. This bilinear form is also connected to the Lagrange product formula. As a corollary, we give a different proof of a theorem of P.J. Olver., 26 pages, in French
- Published
- 2013