Theorems · Theorem · commutative algebra
ascPochhammer_succ_eval
∀ {S : Type u_1} [inst : Semiring S] (n : ℕ) (k : S),
Polynomial.eval k (ascPochhammer S (n + 1)) = Polynomial.eval k (ascPochhammer S n) * (k + ↑n)- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- Polynomialproof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.evalstatement and proof · cited by 796
- mul_addproof · cited by 413
- Polynomial.eval_addproof · cited by 84
- ascPochhammerstatement and proof · cited by 80
- Polynomial.C_eq_natCastproof · cited by 25
- Nat.cast_commproof · cited by 16
- Polynomial.eval_mul_Xproof · cited by 11
- ascPochhammer_succ_rightproof · cited by 11
- Polynomial.eval_C_mulproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- ascPochhammer_eval_eq_zero_iffproof · cited by 3
- ascPochhammer_eval_neg_coe_nat_of_ltproof · cited by 2
- ordinaryHypergeometricSeries_norm_div_succ_normproof · cited by 1