Theorems · Theorem · complex analysis
Complex.integral_circleTransform
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] (R : ℝ) (z w : ℂ) (f : ℂ → E),
∫ (θ : ℝ) in 0..2 * Real.pi, Complex.circleTransform R z w f θ =
(2 * ↑Real.pi * Complex.I)⁻¹ • ∮ (z : ℂ) in C(z, R), (z - w)⁻¹ • f z- Cited by
- 0 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- zero_addproof · cited by 2,366
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- Complex.Istatement and proof · cited by 866
- neg_mulproof · cited by 654
- Complex.expproof · cited by 612
- intervalIntegralstatement and proof · cited by 546
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