proposition: Lemma sin_coeffE x : sin_coeff x = (fun n => (fun n => (odd n)%:R * (-1) ^+ n.-1./2 * (n`!%:R)^-1) n * x ^+ n).
proof: Proof. by apply/funext => i; rewrite /sin_coeff /= -!mulrA [_ / _]mulrC. 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