proposition: Lemma exp_coeffE x : exp_coeff x = (fun n => (fun n => (n`!%:R)^-1) n * x ^+ n).
proof: Proof. by apply/funext => i; rewrite /exp_coeff /= mulrC. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(boolp classical_sets functions) mathcomp(mathcomp_extra) reals ereal signed topology normedtype landau sequences derive realfun itv convex