Theorems · Theorem · complex analysis
Complex.norm_log_one_add_half_le_self
∀ {z : ℂ}, ‖z‖ ≤ 1 / 2 → ‖Complex.log (1 + z)‖ ≤ 3 / 2 * ‖z‖For ‖z‖ ≤ 1/2, the complex logarithm is bounded by (3/2) * ‖z‖.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- le_transproof · cited by 985
- norm_nonnegproof · cited by 725
- lt_of_le_of_ltproof · cited by 432
- le_of_not_gtproof · cited by 430
- lt_of_not_geproof · cited by 374
- mul_le_mul_of_nonneg_leftproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- Complex.summable_log_one_add_of_summableproof · cited by 2
- Summable.hasSumUniformlyOn_log_one_addproof · cited by 1