Theorems · Theorem · special functions
integral_gaussian_complex_Ioi
∀ {b : ℂ}, 0 < b.re → ∫ (x : ℝ) in Set.Ioi 0, Complex.exp (-b * ↑x ^ 2) = (↑Real.pi / b) ^ (1 / 2) / 2- Cited by
- 1 results in Mathlib
- Foundations
- Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Complexstatement and proof · cited by 5,565
- MeasureTheory.integralstatement and proof · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- 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
- Set.Iicproof · cited by 1,111
- Complex.restatement and proof · cited by 882
- neg_mulproof · cited by 654
Cited by1
Results whose statement or proof uses this declaration.
- integral_gaussian_Ioiproof · cited by 1