Theorems · Theorem · harmonic analysis
GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I
∀ {b : ℂ}, 0 < b.re → ∀ (c : ℝ), ∫ (x : ℝ), Complex.exp (-b * (↑x + ↑c * Complex.I) ^ 2) = (↑Real.pi / b) ^ (1 / 2)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites56
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
- nhdsproof · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.Tendstoproof · cited by 3,814
- add_zeroproof · cited by 2,707
- Filter.atTopproof · cited by 2,405
- zero_addproof · cited by 2,366
- MulZeroClass.mul_zeroproof · cited by 2,091
- MeasureTheory.integralstatement · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
Cited by1
Results whose statement or proof uses this declaration.
- integral_cexp_quadraticproof · cited by 5