Mediations on the product rule.
Mémoire sur les développements en fractions continues de la fonction exponentielle, pouvant servir d'introduction à la théorie des fractions continues algébriques
Mémoire sur les séries divergentes
Mercerian and Tauberian Theorems for Differences.
Mercerian theorems for Beekmann matrices.
Mercerian Theorems Involving Cesàro Means of Positive Order.
Mercerian-type theorems for absolute summability
Méthode directe pour calculer la somme des puissances des premiers nombres entiers
Méthode directe pour calculer la somme des puissances des premiers nombres entiers
Mixed Norm Spaces of Difference Sequences and Matrix Transformations
Monoides et semi-anneaux complets.
Monoides et semi-anneaux continus.
Monotonicity of segments of harmonic series ( I )
Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.
More on set-theoretic characteristics of summability of sequences by regular (Toeplitz) matrices
Multigeometric sequences and Cantorvals
For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie...
Multiplication of Series.
Multisommabilité des séries entières solutions formelles d’une équation aux -différences linéaire analytique
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.
Multisummability for some classes of difference equations
This paper concerns difference equations where takes values in and is meromorphic in in a neighborhood of in and holomorphic in a neighborhood of 0 in . It is shown that under certain conditions on the linear part of , formal power series solutions in are multisummable. Moreover, it is shown that formal solutions may always be lifted to holomorphic solutions in upper and lower halfplanes, but in general these solutions are not uniquely determined by the formal solutions.
Multisummability of formal power series solutions of nonlinear meromorphic differential equations
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.