Theorems · Theorem · functional analysis
NormedSpace.expSeries_sum_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), (NormedSpace.expSeries 𝕂 𝔸).sum x = ∑' (n : ℕ), (↑n.factorial)⁻¹ • x ^ n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- 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_eqproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- NormedSpace.exp_eq_tsumproof · cited by 13
- NormedSpace.exp_zeroproof · cited by 8
- NormedSpace.expSeries_sum_eq_ratproof · cited by 1