Theorems · Theorem · real analysis
isLittleO_zpow_exp_pos_mul_atTop
∀ (k : ℤ) {b : ℝ}, 0 < b → (fun x => x ^ k) =o[Filter.atTop] fun x => Real.exp (b * x)x ^ k = o(exp(b * x)) as x → ∞ for any integer k and positive b.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Filter.atTopstatement and proof · cited by 2,405
- Real.expstatement and proof · cited by 871
- Asymptotics.IsLittleOstatement and proof · cited by 375
- Real.rpow_intCastproof · cited by 35
- isLittleO_rpow_exp_pos_mul_atTopproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- isLittleO_pow_exp_pos_mul_atTopproof · cited by 0