Theorems · Theorem · special functions
integrable_cexp_neg_mul_sq
∀ {b : ℂ}, 0 < b.re → MeasureTheory.Integrable (fun x => Complex.exp (-b * ↑x ^ 2)) MeasureTheory.volume- Cited by
- 2 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Complex.ofRealstatement and proof · cited by 1,654
- MeasureTheory.Integrablestatement · cited by 1,367
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Complex.restatement and proof · cited by 882
- Complex.expstatement and proof · cited by 612
- continuous_id'proof · cited by 295
- MeasureTheory.HasFiniteIntegralproof · cited by 120
- Complex.continuous_ofRealproof · cited by 107
- Continuous.comp_aestronglyMeasurableproof · cited by 77
- Continuous.aestronglyMeasurableproof · cited by 70
Cited by2
Results whose statement or proof uses this declaration.
- integral_gaussian_complex_Ioiproof · cited by 1
- GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_Iproof · cited by 1