Theorems · Theorem · complex analysis
Complex.tendsto_one_add_cpow_exp_of_tendsto
∀ {g : ℝ → ℂ} {t : ℂ},
Filter.Tendsto (fun x => ↑x * g x) Filter.atTop (nhds t) →
Filter.Tendsto (fun x => (1 + g x) ^ ↑x) Filter.atTop (nhds (Complex.exp t))The limit of (1 + g x) ^ x as (x : ℝ) → ∞ is exp t,
where t : ℂ is the limit of x * g x.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 276 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
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Nat.cast_oneproof · cited by 2,501
- Filter.atTopstatement and proof · cited by 2,405
- mul_commproof · cited by 2,262
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Complex.ofRealstatement and proof · cited by 1,654
- Filter.mp_memproof · cited by 1,537
- Complex.expstatement and proof · cited by 612
Cited by3
Results whose statement or proof uses this declaration.
- Real.tendsto_one_add_rpow_exp_of_tendstoproof · cited by 2
- Complex.tendsto_one_add_pow_exp_of_tendstoproof · cited by 1
- Complex.tendsto_one_add_div_cpow_expproof · cited by 1