Theorems · Theorem · complex analysis
Complex.norm_exp_sub_sum_le_exp_norm_sub_sum
∀ (x : ℂ) (n : ℕ),
‖Complex.exp x - ∑ m ∈ Finset.range n, x ^ m / ↑m.factorial‖ ≤
Real.exp ‖x‖ - ∑ m ∈ Finset.range n, ‖x‖ ^ m / ↑m.factorial- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 1 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.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Finsetproof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- absproof · cited by 1,814
- Finset.rangestatement and proof · cited by 1,341
- sub_eq_add_negproof · cited by 1,023
- Finset.filterproof · cited by 949
- Real.expstatement and proof · cited by 871
- norm_nonnegproof · cited by 725
Cited by1
Results whose statement or proof uses this declaration.
- Complex.norm_exp_le_exp_normproof · cited by 0