Theorems · Theorem · functional analysis
NormedSpace.expSeries_div_hasSum_exp
∀ {𝔸 : Type u_1} [inst : NormedDivisionRing 𝔸] [NormedAlgebra ℚ 𝔸] [CompleteSpace 𝔸] (x : 𝔸),
HasSum (fun n => x ^ n / ↑n.factorial) (NormedSpace.exp x)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement · cited by 2,068
- NormedAlgebrastatement and proof · cited by 1,165
- Nat.factorialstatement · cited by 616
- HasSumstatement · cited by 518
- NormedDivisionRingstatement and proof · cited by 360
- NormedSpace.expstatement · cited by 157
- edist_lt_topproof · cited by 32
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- NormedSpace.expSeries_div_hasSum_exp_of_mem_ballproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Complex.hasSum_cos'proof · cited by 3
- Complex.hasSum_sin'proof · cited by 3
- ProbabilityTheory.hasSum_one_poissonMeasureproof · cited by 1
- numDerangements_tendsto_inv_eproof · cited by 0
- ProbabilityTheory.charFun_map_cast_poissonMeasureproof · cited by 0