Theorems · Theorem · special functions
Complex.exp_bound_sq
∀ (x z : ℂ), ‖z‖ ≤ 1 → ‖Complex.exp (x + z) - Complex.exp x - z • Complex.exp x‖ ≤ ‖Complex.exp x‖ * ‖z‖ ^ 2
- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- norm_nonnegproof · cited by 725
- Complex.expstatement and proof · cited by 612
- Normproof · cited by 512
- mul_le_mul_of_nonneg_leftproof · cited by 361
- norm_mulproof · cited by 171
- Complex.exp_addproof · cited by 55
- Complex.norm_exp_sub_one_sub_id_leproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Complex.hasDerivAt_expproof · cited by 10
- Complex.locally_lipschitz_expproof · cited by 1