Theorems · Definition · functional analysis
NormedSpace.expSeries
(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] → FormalMultilinearSeries 𝕂 𝔸 𝔸expSeries 𝕂 𝔸 is the FormalMultilinearSeries whose n-th term is the map
(xᵢ) : 𝔸ⁿ ↦ (1/n! : 𝕂) • ∏ xᵢ. Its sum is the exponential map NormedSpace.exp : 𝔸 → 𝔸.
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Nat.factorialproof · cited by 616
- FormalMultilinearSeriesstatement · cited by 615
- IsTopologicalRingstatement and proof · cited by 402
- ContinuousMultilinearMap.mkPiAlgebraFinproof · cited by 29
Cited by69
Results whose statement or proof uses this declaration.
- NormedSpace.expSeries_radius_eq_topstatement · cited by 27
- NormedSpace.expSeries_apply_eqstatement · cited by 12
- NormedSpace.exp_eq_expSeries_sumstatement and proof · cited by 8
- NormedSpace.norm_expSeries_summable_of_mem_ballstatement and proof · cited by 4
- NormedSpace.analyticAt_exp_of_mem_ballstatement and proof · cited by 4
- NormedSpace.norm_expSeries_summable_of_mem_ball'statement and proof · cited by 3
- TrivSqZeroExt.exp_def_of_smul_commproof · cited by 3
- hasStrictFDerivAt_exp_smul_const_of_mem_ballstatement and proof · cited by 3
- hasStrictFDerivAt_exp_zero_of_radius_posstatement and proof · cited by 3
- NormedSpace.expSeries_hasSum_exp_of_mem_ballstatement and proof · cited by 3
- NormedSpace.expSeries_radius_posstatement · cited by 3
- NormedSpace.expSeries_sum_eqstatement · cited by 3