Theorems · Theorem · number theory
hasSum_zeta_nat
∀ {k : ℕ},
k ≠ 0 →
HasSum (fun n => 1 / ↑n ^ (2 * k))
((-1) ^ (k + 1) * 2 ^ (2 * k - 1) * Real.pi ^ (2 * k) * ↑(bernoulli (2 * k)) / ↑(2 * k).factorial)- Defined in
- Mathlib.NumberTheory.ZetaValues
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- pow_oneproof · cited by 894
- Polynomial.mapproof · cited by 806
Cited by3
Results whose statement or proof uses this declaration.
- riemannZeta_two_mul_natproof · cited by 1
- hasSum_zeta_fourproof · cited by 1
- hasSum_zeta_twoproof · cited by 1