Theorems · Theorem · functional analysis
NormedSpace.expSeries_sum_eq_div
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : Field 𝕂] [inst_1 : DivisionRing 𝔸] [inst_2 : Algebra 𝕂 𝔸]
[inst_3 : TopologicalSpace 𝔸] [inst_4 : IsTopologicalRing 𝔸] (x : 𝔸),
(NormedSpace.expSeries 𝕂 𝔸).sum x = ∑' (n : ℕ), x ^ n / ↑n.factorial- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Fieldstatement and proof · cited by 7,404
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- DivisionRingstatement and proof · cited by 1,062
- Nat.factorialstatement · cited by 616
- IsTopologicalRingstatement and proof · cited by 402
- NormedSpace.expSeriesstatement · cited by 68
- tsum_congrproof · cited by 64
- FormalMultilinearSeries.sumstatement · cited by 34
- NormedSpace.expSeries_apply_eq_divproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- NormedSpace.exp_eq_tsum_divproof · cited by 1