A formal calculus on the Riordan skew algebra
Résumé
In this paper the Riordan skew algebra is defined as the semi-direct product "algebra" of the formal power series and the principal ideal generated by the variable x. The Riordan group can be seen as a subgroup of invertible elements of the Riordan skew algebra. It is shown that a formal calculus, playing the same role as the holomorphic calculi for Banach or Fréchet algebras, can be defined on such an algebraic structure. This makes it possible to define in particular some generalized powers for elements of the Riordan group.
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