Theorems · Theorem · special functions
Real.Gamma_eq_integral
∀ {s : ℝ}, 0 < s → Real.Gamma s = ∫ (x : ℝ) in Set.Ioi 0, Real.exp (-x) * x ^ (s - 1)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Complexproof · cited by 5,565
- MeasureTheory.integralstatement and proof · cited by 1,779
- 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
- Complex.reproof · cited by 882
- Real.expstatement and proof · cited by 871
- Real.Gammastatement · cited by 76
- Complex.ofReal_reproof · cited by 34
- Complex.Gamma_eq_integralproof · cited by 6
- RCLike.ofReal_posproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Real.Gamma_pos_of_posproof · cited by 17
- Real.Gamma_one_half_eqproof · cited by 6
- integral_rpow_mul_exp_neg_rpowproof · cited by 4
- Real.Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gammaproof · cited by 1