Theorems · Theorem · special functions
Complex.Gamma_neg_nat_eq_zero
∀ (n : ℕ), Complex.Gamma (-↑n) = 0
At -n for n ∈ ℕ, the Gamma function is undefined; by convention we assign it the value 0.
- 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.
- Complexstatement and proof · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Nat.cast_addproof · cited by 586
- neg_zeroproof · cited by 542
- neg_add_revproof · cited by 236
- mul_ne_zeroproof · cited by 178
- Nat.cast_ne_zeroproof · cited by 113
- Complex.Gammastatement and proof · cited by 96
- neg_ne_zeroproof · cited by 70
- neg_add_cancel_commproof · cited by 17
- Complex.Gamma_add_oneproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- Complex.Gamma_mul_Gamma_one_subproof · cited by 3
- Complex.deriv_Gamma_add_oneproof · cited by 1
- Real.Gamma_neg_nat_eq_zeroproof · cited by 1
- Complex.Gamma_eq_zero_iffproof · cited by 0