Theorems · Theorem · difference equations
fwdDiff_iter_eq_factorial
∀ {R : Type u_3} [inst : CommRing R] {n : ℕ}, ((fwdDiff 1)^[n] fun r => r ^ n) = ↑n.factorialThe n-th forward difference of x ↦ x^n is the constant function n!.
- Defined in
- Mathlib.Algebra.Group.ForwardDiff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 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.
Cites29
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.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Finset.rangeproof · cited by 1,341
- pow_zeroproof · cited by 1,094
- Nat.iteratestatement and proof · cited by 740
- Nat.factorialstatement and proof · cited by 616
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.fwdDiff_iter_degree_eq_factorialproof · cited by 1