Theorems · Theorem · commutative algebra
ascPochhammer_nat_eq_natCast_descFactorial
∀ (S : Type u_1) [inst : Semiring S] (a b : ℕ), Polynomial.eval (↑a) (ascPochhammer S b) = ↑((a + b - 1).descFactorial b)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomial.evalstatement · cited by 796
- ascPochhammerstatement · cited by 80
- Nat.descFactorialstatement and proof · cited by 68
- ascPochhammer_nat_eq_descFactorialproof · cited by 3
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