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_R (a : nat -> R) (x : R) : ex_pseries a x <-> ex_series (fun n : nat => a n * x ^ n).