Theorems · Theorem · functional analysis
NormedSpace.expSeries_apply_eq
∀ {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] (x : 𝔸) (n : ℕ),
((NormedSpace.expSeries 𝕂 𝔸 n) fun x_1 => x) = (↑n.factorial)⁻¹ • x ^ n- Cited by
- 12 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- ContinuousMultilinearMapstatement · cited by 1,016
- Nat.factorialstatement and proof · cited by 616
- IsTopologicalRingstatement and proof · cited by 402
- smul_applyproof · cited by 229
- NormedSpace.expSeriesstatement · cited by 68
- ContinuousMultilinearMap.mkPiAlgebraFinproof · cited by 29
- List.prod_replicateproof · cited by 29
Cited by12
Results whose statement or proof uses this declaration.
- hasStrictFDerivAt_exp_zero_of_radius_posproof · cited by 3
- NormedSpace.expSeries_sum_eqproof · cited by 3
- NormedSpace.expSeries_apply_eq'proof · cited by 2
- NormedSpace.expSeries_apply_eq_divproof · cited by 2
- TrivSqZeroExt.snd_expSeries_of_smul_commproof · cited by 1
- TrivSqZeroExt.hasSum_snd_expSeries_of_smul_commproof · cited by 1
- NormedSpace.exp_continuousMap_eqproof · cited by 1
- TrivSqZeroExt.fst_expSeriesproof · cited by 1
- NormedSpace.expSeries_apply_zeroproof · cited by 1
- Quaternion.expSeries_even_of_imaginaryproof · cited by 1
- Quaternion.expSeries_odd_of_imaginaryproof · cited by 1
- NormedSpace.expSeries_eq_expSeriesproof · cited by 0