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Nous introduisons une version -analogue du procédé d’accélération élémentaire d’Écalle-Martinet-Ramis et définissons la notion de série entière -multisommable. Nous montrons que toute série entière solution formelle d’une équation aux -différences linéaire analytique est -multisommable.
In this paper a proof is given of a theorem of J. Écalle that formal power series solutions of nonlinear meromorphic differential equations are multisummable.
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