Theorems · Theorem · special functions
Real.tendsto_pow_mul_exp_neg_atTop_nhds_zero
∀ (n : ℕ), Filter.Tendsto (fun x => x ^ n * Real.exp (-x)) Filter.atTop (nhds 0)
The function x^n * exp(-x) tends to 0 at +∞, for any natural number n.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- one_mulproof · cited by 2,841
- Filter.atTopstatement · cited by 2,405
- Real.expstatement and proof · cited by 871
- div_eq_mul_invproof · cited by 715
- Filter.Tendsto.compproof · cited by 560
- Filter.Tendsto.congrproof · cited by 70
- inv_eq_one_divproof · cited by 33
- Real.exp_negproof · cited by 28
- tendsto_inv_atTop_zeroproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.tendsto_div_exp_atTopproof · cited by 1