(** Coefficients *)

(* Specifications: *)
Lemma Derive_n_coef (a : nat -> R) (n : nat) :
Rbar_lt (Finite 0) (CV_radius a)
-> Derive_n (PSeries a) n 0 = a n * (INR (fact n)).
Lemma PSeries_ext_recip (a b : nat -> R) (n : nat) :
Rbar_lt (Finite 0) (CV_radius a) -> Rbar_lt (Finite 0) (CV_radius b)
-> locally 0 (fun x => PSeries a x = PSeries b x)
-> a n = b n.
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).