  The Riordan group is the semi-direct product of a multiplicative group of
invertible series and a group, under substitution, of non units. The Riordan
near algebra, as introduced in this paper, is the Cartesian product of the
algebra of formal power series and its principal ideal of non units, equipped
with a product that extends the multiplication of the Riordan group. The later
is naturally embedded as a subgroup of units into the former. In this paper, we
prove the existence of a formal calculus on the Riordan algebra. This formal
calculus plays a role similar to those of holomorphic calculi in the Banach or
Fr\'echet algebras setting, but without the constraint of a radius of
convergence. Using this calculus, we define \emph{en passant} a notion of
generalized powers in the Riordan group.
