Theorems · Theorem · complex analysis
Complex.tendsto_nat_mul_log_one_add_of_tendsto
∀ {g : ℕ → ℂ} {t : ℂ},
Filter.Tendsto (fun n => ↑n * g n) Filter.atTop (nhds t) →
Filter.Tendsto (fun n => ↑n * Complex.log (1 + g n)) Filter.atTop (nhds t)The limit of n * log (1 + g n) as (n : ℝ) → ∞ is t,
where t : ℂ is the limit of n * g n.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 276 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.Tendsto.compproof · cited by 560
- Complex.logstatement and proof · cited by 187
- Filter.Tendsto.congrproof · cited by 70
- tendsto_natCast_atTop_atTopproof · cited by 51
- Nat.floor_natCastproof · cited by 19
- tendsto_smul_comp_nat_floor_of_tendsto_mulproof · cited by 4
- Complex.tendsto_mul_log_one_add_of_tendstoproof · cited by 3
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