Theorems · Theorem · real analysis
intervalIntegral_pow_mul_exp_neg_le
∀ {k : ℕ} {M c : ℝ}, 0 ≤ M → 0 < c → ∫ (x : ℝ) in 0..M, x ^ k * Real.exp (-(c * x)) ≤ ↑k.factorial / c ^ (k + 1)- Defined in
- Mathlib.Analysis.SumIntegralExpDecay
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- MeasureTheory.integralproof · cited by 1,779
- Filter.univ_mem'proof · cited by 1,672
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Filter.mp_memproof · cited by 1,537
- Set.Ioiproof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Set.Iocproof · cited by 971
Cited by1
Results whose statement or proof uses this declaration.
- sum_Ico_pow_mul_exp_neg_leproof · cited by 1