Theorems · Theorem · field theory
Polynomial.coeff_X_add_C_pow
∀ {R : Type u} [inst : Semiring R] (r : R) (n k : ℕ),
((Polynomial.X + Polynomial.C r) ^ n).coeff k = r ^ (n - k) * ↑(n.choose k)- Defined in
- Mathlib.Algebra.Polynomial.Coeff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 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.
Cites25
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- 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
- Polynomial.Xstatement and proof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.Cstatement and proof · cited by 1,598
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.coeff_X_add_one_powproof · cited by 4