Theorems · Theorem · measure theory
Complex.integral_exp_neg_mul_rpow
∀ {p b : ℝ}, 1 ≤ p → 0 < b → ∫ (x : ℂ), Real.exp (-b * ‖x‖ ^ p) = Real.pi * b ^ (-2 / p) * Real.Gamma (2 / p + 1)- Defined in
- Mathlib.MeasureTheory.Integral.Gamma
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- MeasureTheory.integralstatement and proof · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Real.expstatement and proof · cited by 871
- lt_of_not_geproof · cited by 374
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.convexBodySum_volumeproof · cited by 1