Theorems · Theorem · real analysis
integral_cos_mul_complex
∀ {z : ℂ},
z ≠ 0 → ∀ (a b : ℝ), ∫ (x : ℝ) in a..b, Complex.cos (z * ↑x) = Complex.sin (z * ↑b) / z - Complex.sin (z * ↑a) / z- Cited by
- 1 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.MeasureSpace.volumestatement · cited by 1,323
- intervalIntegralstatement · cited by 546
- HasDerivAtproof · cited by 493
- Set.uIccproof · cited by 393
- Complex.cosstatement and proof · cited by 279
- Complex.sinstatement and proof · cited by 258
- Continuous.comp'proof · cited by 184
- Complex.continuous_ofRealproof · cited by 107
- HasDerivAt.compproof · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- EulerSine.sin_pi_mul_eqproof · cited by 1