proposition: Lemma cosE : cos = fun x => lim (series (fun n => (fun n => (~~(odd n))%:R * (-1)^+ n./2 * (n`!%:R)^-1) n * x ^+ n) @ \oo).
proof: Proof. by apply/funext => x; rewrite -cos_coeffE. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) reals ereal nsatz_realtype signed topology normedtype landau sequences derive realfun exp