Theorems · Theorem · measure theory
integral_rpow_mul_exp_neg_rpow
∀ {p q : ℝ}, 0 < p → -1 < q → ∫ (x : ℝ) in Set.Ioi 0, x ^ q * Real.exp (-x ^ p) = 1 / p * Real.Gamma ((q + 1) / p)- Defined in
- Mathlib.MeasureTheory.Integral.Gamma
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- MeasureTheory.integralstatement and proof · cited by 1,779
- mul_assocproof · cited by 1,667
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- le_of_ltproof · cited by 1,175
- pow_oneproof · cited by 894
Cited by4
Results whose statement or proof uses this declaration.
- integral_rpow_mul_exp_neg_mul_rpowproof · cited by 2
- integral_exp_neg_rpowproof · cited by 2
- MeasureTheory.measure_unitBall_eq_integral_div_gammaproof · cited by 1
- Complex.integral_rpow_mul_exp_neg_rpowproof · cited by 1