Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars_sum_eq
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Field 𝕜] [inst_1 : Ring E] [inst_2 : Algebra 𝕜 E] [inst_3 : TopologicalSpace E]
[inst_4 : IsTopologicalRing E] (c : ℕ → 𝕜) (x : E), FormalMultilinearSeries.ofScalarsSum c x = ∑' (n : ℕ), c n • x ^ n- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- IsTopologicalRingstatement and proof · cited by 402
- tsum_congrproof · cited by 64
- FormalMultilinearSeries.ofScalarsSumstatement · cited by 8
- FormalMultilinearSeries.ofScalars_apply_eqproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.ofScalarsSum_eq_tsumproof · cited by 2
- FormalMultilinearSeries.ofScalarsSum_opproof · cited by 0
- FormalMultilinearSeries.ofScalarsSum_unopproof · cited by 0