Theorems · Theorem · measure theory
Complex.integral_rpow_mul_exp_neg_mul_rpow
∀ {p q b : ℝ},
1 ≤ p →
-2 < q →
0 < b →
∫ (x : ℂ), ‖x‖ ^ q * Real.exp (-b * ‖x‖ ^ p) = 2 * Real.pi / p * b ^ (-(q + 2) / p) * Real.Gamma ((q + 2) / p)- Defined in
- Mathlib.MeasureTheory.Integral.Gamma
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites52
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupproof · cited by 15,752
- MeasurableSpaceproof · cited by 13,106
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
Cited by1
Results whose statement or proof uses this declaration.
- Complex.integral_exp_neg_mul_rpowproof · cited by 1