Theorems · Theorem · special functions
integral_gaussian_complex
∀ {b : ℂ}, 0 < b.re → ∫ (x : ℝ), Complex.exp (-b * ↑x ^ 2) = (↑Real.pi / b) ^ (1 / 2)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites60
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- MeasureTheory.integralstatement and proof · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
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