Theorems · Theorem · real analysis
Complex.continuousAt_cpow_const_of_re_pos
∀ {z w : ℂ}, 0 ≤ z.re ∨ z.im ≠ 0 → 0 < w.re → ContinuousAt (fun x => x ^ w) zSee also continuousAt_cpow_const for a version that assumes z ≠ 0 but makes no
assumptions about w.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 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.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.restatement and proof · cited by 882
- ContinuousAtstatement · cited by 697
- Complex.imstatement and proof · cited by 591
- Filter.Tendsto.compproof · cited by 560
- continuousAt_constproof · cited by 59
- continuousAt_idproof · cited by 28
- ContinuousAt.prodMkproof · cited by 18
- Complex.continuousAt_cpow_of_re_posproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Complex.continuousAt_sqrtproof · cited by 1
- Complex.betaIntegral_recurrenceproof · cited by 1