Theorems · Theorem · special functions
Complex.Gamma_nat_eq_factorial
∀ (n : ℕ), Complex.Gamma (↑n + 1) = ↑n.factorial
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 286 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.
- Complexstatement and proof · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Nat.factorialstatement and proof · cited by 616
- CharP.cast_eq_zeroproof · cited by 357
- Nat.cast_mulproof · cited by 309
- Nat.cast_ne_zeroproof · cited by 113
- Nat.cast_succproof · cited by 99
- Complex.Gammastatement and proof · cited by 96
- Complex.Gamma_add_oneproof · cited by 12
- Complex.Gamma_oneproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Real.Gamma_nat_eq_factorialproof · cited by 5
- HurwitzZeta.cosZeta_two_mul_nat'proof · cited by 1
- HurwitzZeta.sinZeta_two_mul_nat_add_one'proof · cited by 1
- Complex.Gamma_ofNat_eq_factorialproof · cited by 0