Theorems · Theorem · functional analysis
NormedSpace.exp_eq_expSeries_sum
∀ (𝕂 : Type u_1) {𝔸 : Type u_2} [inst : Field 𝕂] [inst_1 : Ring 𝔸] [inst_2 : Algebra 𝕂 𝔸] [inst_3 : TopologicalSpace 𝔸]
[inst_4 : IsTopologicalRing 𝔸] [CharZero 𝕂], NormedSpace.exp = (NormedSpace.expSeries 𝕂 𝔸).sum- Cited by
- 8 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CharZerostatement and proof · cited by 932
- IsTopologicalRingstatement and proof · cited by 402
- NormedSpace.expstatement · cited by 157
- NormedSpace.expSeriesstatement and proof · cited by 68
- FormalMultilinearSeries.sumstatement and proof · cited by 34
- NormedSpace.exp_defproof · cited by 3
- NormedSpace.expSeries_sum_eq_ratproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- NormedSpace.exp_eq_tsumproof · cited by 13
- NormedSpace.hasFPowerSeriesOnBall_exp_of_radius_posproof · cited by 3
- NormedSpace.expSeries_hasSum_exp_of_mem_ballproof · cited by 3
- TrivSqZeroExt.exp_def_of_smul_commproof · cited by 3
- NormedSpace.continuousOn_expproof · cited by 1
- NormedSpace.exp_continuousMap_eqproof · cited by 1
- NormedSpace.exp_eq_tsum_divproof · cited by 1
- Complex.regularizedHGFun_zero_zeroproof · cited by 0