Theorems · Theorem · complex analysis
Complex.norm_log_one_sub_inv_add_logTaylor_neg_le
∀ (n : ℕ) {z : ℂ},
‖z‖ < 1 → ‖Complex.log (1 - z)⁻¹ + Complex.logTaylor (n + 1) (-z)‖ ≤ ‖z‖ ^ (n + 1) * (1 - ‖z‖)⁻¹ / (↑n + 1)The difference of log (1-z)⁻¹ and its (n+1)st Taylor polynomial can be bounded in
terms of ‖z‖.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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
- sub_eq_add_negproof · cited by 1,023
- sub_neg_eq_addproof · cited by 264
- norm_negproof · cited by 190
- Complex.logstatement and proof · cited by 187
- Complex.logTaylorstatement and proof · cited by 12
- neg_sub'proof · cited by 10
- Complex.mem_slitPlane_of_norm_lt_oneproof · cited by 5
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
- Complex.log_invproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Complex.norm_log_one_sub_inv_sub_self_leproof · cited by 0