(** ** Definition of the arctangent function as the sum of the arctan power series *)

(* Proof taken from Guillaume Melquiond's interval package for Coq *)

Definition Ratan_seq x :=  fun n => (x ^ (2 * n + 1) / INR (2 * n + 1))%R.

(* Specifications: *)
Lemma Ratan_seq_decreasing : forall x, (0 <= x <= 1)%R -> Un_decreasing (Ratan_seq x).
Lemma Ratan_seq_converging : forall x, (0 <= x <= 1)%R -> Un_cv (Ratan_seq x) 0.