Theorems · Theorem · special functions
Complex.Gamma_add_nat_div_Gamma_eq
∀ {n : ℕ} (z : ℂ),
(∀ (k : ℕ), z ≠ -↑k) → Complex.Gamma (z + ↑n) / Complex.Gamma z = Polynomial.eval z (ascPochhammer ℂ n)The ascending Pochhammer symbol is given by the ratio of Γ functions.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Polynomial.evalstatement and proof · cited by 796
- Nat.cast_addproof · cited by 586
- CharP.cast_eq_zeroproof · cited by 357
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_mulproof · cited by 127
- Complex.Gammastatement and proof · cited by 96
- Polynomial.eval_oneproof · cited by 86
- Polynomial.eval_addproof · cited by 84
- ascPochhammerstatement and proof · cited by 80
Cited by1
Results whose statement or proof uses this declaration.
- Complex.Gamma_inv_mul_ordinaryHypergeometricSeries_eqproof · cited by 1