Theorems · Theorem · difference equations
Polynomial.fwdDiff_iter_degree_eq_factorial
∀ {R : Type u_3} [inst : CommRing R] (P : Polynomial R),
((fwdDiff 1)^[P.natDegree] fun x => Polynomial.eval x P) = P.leadingCoeff • ↑P.natDegree.factorial- Defined in
- Mathlib.Algebra.Group.ForwardDiff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 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.
Cites25
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
- Finsetproof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.evalstatement · cited by 796
- Nat.iteratestatement and proof · cited by 740
- smul_zeroproof · cited by 665
- Nat.factorialstatement and proof · cited by 616
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.fwdDiff_iter_eq_zero_of_degree_ltproof · cited by 1