Theorems · Theorem · complex analysis
AnalyticWithinAt.cpow
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f g : E → ℂ} {x : E} {s : Set E},
AnalyticWithinAt ℂ f s x →
AnalyticWithinAt ℂ g s x → f x ∈ Complex.slitPlane → AnalyticWithinAt ℂ (fun z => f z ^ g z) s xf z ^ g z is analytic if f z is not a nonpositive real
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- nhdsWithinproof · cited by 1,912
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Complex.expproof · cited by 612
- Complex.logproof · cited by 187
- Complex.slitPlanestatement and proof · cited by 113
- AnalyticWithinAtstatement and proof · cited by 96
Cited by2
Results whose statement or proof uses this declaration.
- AnalyticOn.cpowproof · cited by 1
- AnalyticAt.cpowproof · cited by 1