Theorems · Theorem · number theory
HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat
∀ {k : ℕ} {x : ℝ},
k ≠ 0 →
x ∈ Set.Icc 0 1 →
HurwitzZeta.hurwitzZetaEven (↑x) (1 - 2 * ↑k) =
-1 / (2 * ↑k) * Polynomial.eval (↑x) (Polynomial.map (algebraMap ℚ ℂ) (Polynomial.bernoulli (2 * k)))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- Real.piproof · cited by 1,774
- Set.Iccstatement and proof · cited by 1,702
- mul_assocproof · cited by 1,667
- Complex.ofRealstatement and proof · cited by 1,654
- neg_negproof · cited by 960
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.