Theorems · Theorem · special functions
Complex.betaIntegral_scaled
∀ (s t : ℂ) {a : ℝ}, 0 < a → ∫ (x : ℝ) in 0..a, ↑x ^ (s - 1) * (↑a - ↑x) ^ (t - 1) = ↑a ^ (s + t - 1) * s.betaIntegral t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measureproof · cited by 10,939
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- mul_assocproof · cited by 1,667
- Complex.ofRealstatement and proof · cited by 1,654
- LT.lt.ne'proof · cited by 1,417
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
Cited by1
Results whose statement or proof uses this declaration.
- Complex.Gamma_mul_Gamma_eq_betaIntegralproof · cited by 1