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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) z

See also continuousAt_cpow_const for a version that assumes z ≠ 0 but makes no assumptions about w.

Defined in
Mathlib.Analysis.SpecialFunctions.Pow.Continuity
Cited by
2 results in Mathlib
Foundations
Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

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