Theorems · Theorem · special functions
Complex.GammaIntegral_ofReal
∀ (s : ℝ), (↑s).GammaIntegral = ↑(∫ (x : ℝ) in Set.Ioi 0, Real.exp (-x) * x ^ (s - 1))
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- LT.lt.leproof · cited by 2,189
- MeasureTheory.integralstatement and proof · cited by 1,779
- Complex.ofRealstatement and proof · cited by 1,654
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Set.Ioistatement and proof · cited by 1,463
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Real.expstatement and proof · cited by 871
- Complex.expproof · cited by 612
- RCLike.ofRealproof · cited by 350
- Complex.ofReal_mulproof · cited by 180
Cited by2
Results whose statement or proof uses this declaration.
- Real.Gamma_eq_integralproof · cited by 4
- Complex.GammaIntegral_oneproof · cited by 1