Theorems · Theorem · number theory
HurwitzZeta.hasSum_int_oddKernel
∀ (a : ℝ) {x : ℝ},
0 < x → HasSum (fun n => (↑n + a) * Real.exp (-Real.pi * (↑n + a) ^ 2 * x)) (HurwitzZeta.oddKernel (↑a) x)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- mul_assocproof · cited by 1,667
- Complex.ofRealproof · cited by 1,654
- pow_oneproof · cited by 894
- Real.expstatement and proof · cited by 871
- Complex.Iproof · cited by 866
Cited by2
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_int_completedHurwitzZetaOddproof · cited by 1
- HurwitzZeta.isBigO_atTop_oddKernelproof · cited by 0