Theorems · Theorem · field theory
Polynomial.taylor_coeff
∀ {R : Type u_1} [inst : Semiring R] (r : R) (f : Polynomial R) (n : ℕ),
((Polynomial.taylor r) f).coeff n = Polynomial.eval r ((Polynomial.hasseDeriv n) f)The kth coefficient of Polynomial.taylor r f is (Polynomial.hasseDeriv k f).eval r.
- Defined in
- Mathlib.Algebra.Polynomial.Taylor
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 109 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.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement and proof · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.taylor_coeff_zeroproof · cited by 2
- Polynomial.coeff_taylor_natDegreeproof · cited by 2
- Polynomial.taylor_coeff_oneproof · cited by 1
- Polynomial.eq_zero_of_hasseDeriv_eq_zeroproof · cited by 0