Theorems · Theorem · functional analysis
hasDerivAt_exp_of_mem_ball
∀ {𝕂 : Type u_1} [inst : NontriviallyNormedField 𝕂] [CompleteSpace 𝕂] [CharZero 𝕂] {x : 𝕂},
x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝕂).radius → HasDerivAt NormedSpace.exp (NormedSpace.exp x) xThe exponential map in a complete normed field 𝕂 of characteristic zero has derivative
NormedSpace.exp x at any point x in the disk of convergence.
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- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- CharZerostatement and proof · cited by 932
- HasDerivAtstatement · cited by 493
- Metric.eballstatement and proof · cited by 294
- NormedSpace.expstatement · cited by 157
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
- NormedSpace.expSeriesstatement and proof · cited by 68
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- hasStrictDerivAt_exp_of_mem_ballproof · cited by 2
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