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

Lemma is_derive_2_Bessel1 (n : nat) (x : R) : is_derive_n (Bessel1 n) 2 x (((x/2)^(S (S n)) * PSeries (PS_derive (PS_derive (Bessel1_seq n))) ((x / 2) ^ 2)) + ((INR (2*n+1)/2) * (x/2)^n * PSeries (PS_derive (Bessel1_seq n)) ((x / 2) ^ 2)) + (INR (n * pred n) / 4 * (x / 2) ^ pred (pred n) * PSeries (Bessel1_seq n) ((x / 2) ^ 2))).