proposition: Lemma is_cvg_series_cos_coeff x : cvg (series (cos_coeff x) @ \oo).
proof: Proof. apply: normed_cvg. apply: series_le_cvg; last exact: (@is_cvg_series_exp_coeff _ `|x|). - by move=> n; rewrite normr_ge0. - by move=> n; rewrite divr_ge0. - move=> n /=; rewrite /exp_coeff /cos_coeff /=. rewrite !normrM normfV !normr_nat !normrX normrN normr1 expr1n mulr1. by case: odd; [rewrite !mul0r | rewrite mul1r]. 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