(** Coefficients *)

Lemma mk_pseries (f : R -> R) (M : R) (r : Rbar) :
(forall n x, Rbar_lt (Finite (Rabs x)) r
-> (ex_derive_n f n x) /\ Rabs (Derive_n f n x) <= M)
-> forall x, Rbar_lt (Finite (Rabs x)) r
-> is_pseries (fun n => Derive_n f n 0 / INR (fact n))  x (f x).