Definition is_pseries (a : nat -> V) (x:K) (l : V) :=
  is_series (fun k => scal (pow_n x k) (a k)) l.Definition ex_pseries (a : nat -> V) (x : K) :=
  ex_series (fun k => scal (pow_n x k) (a k)).Definition PSeries (a : nat -> R) (x : R) : R :=
  Series (fun k => a k * x ^ k).

Lemma ex_pseries_ext (a b : nat -> V) (x : K) : (forall n, a n = b n) -> ex_pseries a x -> ex_pseries b x.