Theorems · Theorem · commutative algebra
ascPochhammer_nat_eq_descFactorial
∀ (a b : ℕ), Polynomial.eval a (ascPochhammer ℕ b) = (a + b - 1).descFactorial b
- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Polynomial.evalstatement · cited by 796
- ascPochhammerstatement · cited by 80
- Nat.descFactorialstatement and proof · cited by 68
- Nat.ascFactorialproof · cited by 41
- ascPochhammer_nat_eq_ascFactorialproof · cited by 6
- Nat.add_descFactorial_eq_ascFactorial'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- summable_pow_mul_geometric_of_norm_lt_oneproof · cited by 1
- Nat.cast_descFactorialproof · cited by 1
- ascPochhammer_nat_eq_natCast_descFactorialproof · cited by 0