Theorems · Theorem · functional analysis
NormedSpace.expSeries_apply_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) (n : ℕ),
((NormedSpace.expSeries 𝕂 𝔸 n) fun x_1 => x) = x ^ n / ↑n.factorial- Cited by
- 2 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- DivisionRingstatement and proof · cited by 1,062
- ContinuousMultilinearMapstatement · cited by 1,016
- div_eq_mul_invproof · cited by 715
- Nat.factorialstatement and proof · cited by 616
- IsTopologicalRingstatement and proof · cited by 402
- smul_eq_mulproof · cited by 357
- Commute.eqproof · cited by 91
- NormedSpace.expSeriesstatement and proof · cited by 68
Cited by2
Results whose statement or proof uses this declaration.
- NormedSpace.expSeries_apply_eq_div'proof · cited by 2
- NormedSpace.expSeries_sum_eq_divproof · cited by 1