Theorems · Theorem · complex analysis
Meromorphic.fun_sum
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {ι : Type u_5} {s : Finset ι} {G : ι → 𝕜 → E},
(∀ σ ∈ s, Meromorphic (G σ)) → Meromorphic fun a => ∑ c ∈ s, G c aEta-expanded form of Meromorphic.sum
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.sumstatement · cited by 5,195
- Meromorphicstatement and proof · cited by 108
- Finset.sum_fnproof · cited by 21
- Meromorphic.sumproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ValueDistribution.proximity_sum_top_leproof · cited by 2