Theorems · Theorem · number theory
HurwitzZeta.hasSum_int_hurwitzZetaOdd
∀ (a : ℝ) {s : ℂ},
1 < s.re → HasSum (fun n => ↑(SignType.sign (↑n + a)) / ↑|↑n + a| ^ s / 2) (HurwitzZeta.hurwitzZetaOdd (↑a) s)Formula for hurwitzZetaOdd as a Dirichlet series in the convergence range (sum over ℤ).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalstatement · cited by 2,068
- absstatement and proof · cited by 1,814
- Complex.ofRealstatement and proof · cited by 1,654
- OrderHomstatement · cited by 934
- Complex.restatement and proof · cited by 882
- HasSumstatement · cited by 518
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement · cited by 348
Cited by1
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_nat_hurwitzZetaOddproof · cited by 1