Theorems · Theorem · special functions
Complex.Gamma_ne_zero
∀ {s : ℂ}, (∀ (m : ℕ), s ≠ -↑m) → Complex.Gamma s ≠ 0The Gamma function does not vanish on ℂ (except at non-positive integers, where the function
is mathematically undefined and we set it to 0 by convention).
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- add_zeroproof · cited by 2,707
- Real.piproof · cited by 1,774
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- LT.lt.ne'proof · cited by 1,417
- Complex.reproof · cited by 882
- Complex.Iproof · cited by 866
- Complex.improof · cited by 591
- Complex.sinproof · cited by 258
- Complex.ofReal_mulproof · cited by 180
Cited by6
Results whose statement or proof uses this declaration.
- Complex.differentiable_one_div_Gammaproof · cited by 4
- Complex.Gamma_ne_zero_of_re_posproof · cited by 2
- HurwitzZeta.hurwitzZetaOdd_neg_two_mul_natproof · cited by 0
- HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_natproof · cited by 0
- Complex.digamma_apply_add_oneproof · cited by 0
- Complex.Gamma_eq_zero_iffproof · cited by 0