Definition Bessel1 (n : nat) (x : R) :=
  (x/2)^n * PSeries (Bessel1_seq n) ((x/2)^2).

Lemma Bessel1_uniqueness_aux_1 (a : nat -> R) (n : nat) : (a 0%nat = 0 \/ n = O) -> (a 1%nat = 0 \/ n = 1%nat) -> (forall k, (INR (S (S k)) ^ 2 - INR n ^ 2) * a (S (S k)) + a k = 0) -> (forall k : nat, (k < n)%nat -> a k = 0) /\ (forall p : nat, a (n + 2 * p + 1)%nat = 0) /\ (forall p : nat, a (n + 2 * p)%nat = Bessel1_seq n p * / 2 ^ (2 * p) * INR (fact n) * a n).