Theorems · Theorem · several complex variables
FormalMultilinearSeries.analyticAt_changeOrigin
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [CompleteSpace F]
(p : FormalMultilinearSeries 𝕜 E F), p.radius > 0 → ∀ (n : ℕ), AnalyticAt 𝕜 (fun x => p.changeOrigin x n) 0Power series terms are analytic as we vary the origin
- Defined in
- Mathlib.Analysis.Analytic.ChangeOrigin
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMultilinearMapstatement · cited by 1,016
- FormalMultilinearSeriesstatement and proof · cited by 615
- AnalyticAtstatement · cited by 321
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- FormalMultilinearSeries.changeOriginstatement · cited by 27
- FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOriginproof · cited by 4
- HasFPowerSeriesOnBall.analyticAtproof · cited by 4
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