Definition PS_mult (a b : nat -> R) n :=
  sum_f_R0 (fun k => a k * b (n - k)%nat) n.

Lemma is_pseries_mult (a b : nat -> R) (x la lb : R) : is_pseries a x la -> is_pseries b x lb -> Rbar_lt (Rabs x) (CV_radius a) -> Rbar_lt (Rabs x) (CV_radius b) -> is_pseries (PS_mult a b) x (la * lb).