Theorems · Theorem · several complex variables
HasFPowerSeriesOnBall.analyticAt
∀ {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] {f : E → F}
{p : FormalMultilinearSeries 𝕜 E F} {x : E} {r : ENNReal}, HasFPowerSeriesOnBall f p x r → AnalyticAt 𝕜 f x- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- FormalMultilinearSeriesstatement and proof · cited by 615
- AnalyticAtstatement · cited by 321
- HasFPowerSeriesOnBallstatement and proof · cited by 131
- HasFPowerSeriesOnBall.hasFPowerSeriesAtproof · cited by 18
- HasFPowerSeriesAt.analyticAtproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- DifferentiableOn.analyticAtproof · cited by 6
- AnalyticAt.fderivproof · cited by 1
- Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAtproof · cited by 1
- FormalMultilinearSeries.analyticAt_changeOriginproof · cited by 0