Theorems · Theorem · commutative algebra
descPochhammer_eval_eq_ascPochhammer
∀ (R : Type u) [inst : Ring R] (r : R) (n : ℕ), Polynomial.eval r (descPochhammer R n) = Polynomial.eval (r - ↑n + 1) (ascPochhammer R n)
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Polynomial.Xproof · cited by 1,639
- Polynomial.mapproof · cited by 806
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.eval₂proof · cited by 267
- Polynomial.compproof · cited by 193
- add_sub_cancel_rightproof · cited by 187
- Polynomial.map_Xproof · cited by 122
- Nat.cast_succproof · cited by 99
- Polynomial.eval_oneproof · cited by 86
Cited by4
Results whose statement or proof uses this declaration.
- binomialSeries_eq_ordinaryHypergeometricSeriesproof · cited by 2
- descPochhammer_nonnegproof · cited by 2
- descPochhammer_posproof · cited by 1
- descPochhammer_eval_coe_nat_of_ltproof · cited by 0