Theorems · Theorem · complex analysis
Complex.tendsto_mul_log_one_add_of_tendsto
∀ {g : ℝ → ℂ} {t : ℂ},
Filter.Tendsto (fun x => ↑x * g x) Filter.atTop (nhds t) →
Filter.Tendsto (fun x => ↑x * Complex.log (1 + g x)) Filter.atTop (nhds t)The limit of x * log (1 + g x) as (x : ℝ) → ∞ is t,
where t : ℂ is the limit of x * g x.
- Cited by
- 3 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.
Cites34
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
- nhdsstatement and proof · cited by 5,554
- Norm.normproof · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- one_mulproof · cited by 2,841
- Filter.atTopstatement and proof · cited by 2,405
- Nat.cast_zeroproof · cited by 1,870
- Filter.univ_mem'proof · cited by 1,672
- Complex.ofRealstatement and proof · cited by 1,654
- Filter.mp_memproof · cited by 1,537
- one_ne_zeroproof · cited by 885
Cited by3
Results whose statement or proof uses this declaration.
- Complex.tendsto_one_add_cpow_exp_of_tendstoproof · cited by 3
- Real.tendsto_mul_log_one_add_of_tendstoproof · cited by 2
- Complex.tendsto_nat_mul_log_one_add_of_tendstoproof · cited by 0