Theorems · Theorem · functional analysis
NormedSpace.exp_eq_tsum
∀ (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] [CharZero 𝕂], NormedSpace.exp = fun x => ∑' (n : ℕ), (↑n.factorial)⁻¹ • x ^ n- Cited by
- 13 results in Mathlib
- Foundations
- Depth 86 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 and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- CharZerostatement and proof · cited by 932
- Nat.factorialstatement and proof · cited by 616
- IsTopologicalRingstatement and proof · cited by 402
- NormedSpace.expstatement · cited by 157
- NormedSpace.exp_eq_expSeries_sumproof · cited by 8
- NormedSpace.expSeries_sum_eqproof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- Commute.exp_rightproof · cited by 4
- NormedSpace.star_expproof · cited by 4
- NormedSpace.exp_eq_tsum_ratproof · cited by 4
- NormedSpace.exp_add_of_commute_of_mem_ballproof · cited by 3
- NormedSpace.map_exp_of_mem_ballproof · cited by 2
- Quaternion.exp_of_re_eq_zeroproof · cited by 1
- SemiconjBy.exp_rightproof · cited by 1
- spectrum.exp_mem_expproof · cited by 1
- NormedSpace.exp_continuousMap_eqproof · cited by 1
- NormedSpace.exp_memproof · cited by 1
- NormedSpace.exp_opproof · cited by 1
- Real.cosh_le_exp_half_sqproof · cited by 0