Theorems · Theorem · number theory
Polynomial.bernoulli_comp_neg_X
∀ (n : ℕ), (Polynomial.bernoulli n).comp (-Polynomial.X) = (-1) ^ n • (Polynomial.bernoulli n + n • Polynomial.X ^ (n - 1))
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- Polynomial.Xstatement and proof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- one_smulproof · cited by 1,374
- pow_zeroproof · cited by 1,094
- Polynomial.coeffproof · cited by 1,045
- smul_zeroproof · cited by 665
- Nat.cast_addproof · cited by 586
- Nat.chooseproof · cited by 494
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.bernoulli_comp_one_sub_Xproof · cited by 2
- Polynomial.bernoulli_eval_negproof · cited by 0