Theorems · Theorem · commutative algebra
descPochhammer_eval_eq_prod_range
∀ {R : Type u_1} [inst : CommRing R] (n : ℕ) (r : R),
Polynomial.eval r (descPochhammer R n) = ∏ j ∈ Finset.range n, (r - ↑j)- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finset.prodstatement and proof · cited by 2,356
- Polynomial.Xproof · cited by 1,639
- Finset.rangestatement and proof · cited by 1,341
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.eval_Xproof · cited by 172
- Polynomial.eval_mulproof · cited by 127
- Polynomial.eval_subproof · cited by 124
- Polynomial.eval_oneproof · cited by 86
- descPochhammerstatement and proof · cited by 51
- Polynomial.eval_natCastproof · cited by 24
- descPochhammer_succ_rightproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- differentiable_descPochhammer_evalproof · cited by 2
- deriv_descPochhammer_eval_eq_sum_prod_range_eraseproof · cited by 1