Theorems · Theorem · special functions
Real.Gamma_add_one
∀ {s : ℝ}, s ≠ 0 → Real.Gamma (s + 1) = s * Real.Gamma s- Cited by
- 13 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.
Cites11
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
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Complex.Gammaproof · cited by 96
- Complex.ofReal_addproof · cited by 94
- Real.Gammastatement · cited by 76
- Complex.ofReal_ne_zeroproof · cited by 46
- Complex.ofReal_oneproof · cited by 43
- Complex.re_ofReal_mulproof · cited by 20
- Complex.Gamma_add_oneproof · cited by 12
Cited by13
Results whose statement or proof uses this declaration.
- Real.Gamma_ne_zeroproof · cited by 3
- Real.Gamma_nat_add_one_add_halfproof · cited by 2
- Real.deriv_Gamma_natproof · cited by 2
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- EuclideanSpace.volume_ballproof · cited by 2
- integral_exp_neg_rpowproof · cited by 2
- NumberField.mixedEmbedding.convexBodySum_volumeproof · cited by 1
- MeasureTheory.measure_unitBall_eq_integral_div_gammaproof · cited by 1
- Real.BohrMollerup.tendsto_log_gammaproof · cited by 1
- Complex.integral_exp_neg_mul_rpowproof · cited by 1
- Complex.integral_exp_neg_rpowproof · cited by 1
- Real.doublingGamma_add_oneproof · cited by 1