Theorems · Theorem · real analysis
integral_exp_mul_complex_Ioi
∀ {a : ℂ}, a.re < 0 → ∀ (c : ℝ), ∫ (x : ℝ) in Set.Ioi c, Complex.exp (a * ↑x) = -Complex.exp (a * ↑c) / a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 282 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.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- MulZeroClass.mul_zeroproof · cited by 2,091
- MeasureTheory.integralstatement · cited by 1,779
- Complex.ofRealstatement and proof · cited by 1,654
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Set.Ioistatement · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- sub_zeroproof · cited by 938
Cited by2
Results whose statement or proof uses this declaration.
- integral_exp_mul_Ioiproof · cited by 1
- integral_exp_mul_complex_Iicproof · cited by 0