Theorems · Theorem · special functions
integral_gaussian
∀ (b : ℝ), ∫ (x : ℝ), Real.exp (-b * x ^ 2) = √(Real.pi / b)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 289 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- NormedAddCommGroupproof · cited by 15,752
- MeasurableSpaceproof · cited by 13,106
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- Complexproof · cited by 5,565
- LT.lt.leproof · cited by 2,189
- MeasureTheory.integralstatement and proof · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealproof · cited by 1,654
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- le_of_ltproof · cited by 1,175
Cited by2
Results whose statement or proof uses this declaration.
- integral_gaussian_complexproof · cited by 2
- ProbabilityTheory.lintegral_gaussianPDFReal_eq_oneproof · cited by 2