Theorems · Theorem · complex analysis
HasSum.hasSum_at_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] (a : ℕ → E), HasSum (fun n => 0 ^ n • a n) (a 0)- Defined in
- Mathlib.Analysis.Analytic.IsolatedZeros
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpaceproof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddCommMonoidproof · cited by 12,281
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- one_smulproof · cited by 1,374
- pow_zeroproof · cited by 1,094
- zero_smulproof · cited by 716
- SummationFilterproof · cited by 607
- HasSumstatement and proof · cited by 518
- zero_powproof · cited by 361
Cited by1
Results whose statement or proof uses this declaration.
- HasSum.exists_hasSum_smul_of_apply_eq_zeroproof · cited by 0