Theorems · Theorem · complex analysis
circleIntegrable_sub_zpow_iff
∀ {c w : ℂ} {R : ℝ} {n : ℤ}, CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ Metric.sphere c |R|The function fun z ↦ (z - w) ^ n, n : ℤ, is circle integrable on the circle with center c
and radius |R| if and only if R = 0 or 0 ≤ n, or w does not belong to this circle.
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- Foundations
- Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
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