Theorems · Theorem · complex analysis
Complex.meromorphicOrderAt_canonicalFactor
∀ {R : ℝ} {w : ℂ}, w ∈ Metric.ball 0 R → meromorphicOrderAt (Complex.canonicalFactor R w) w = -1The canonical factor CanonicalFactor R w has a simple pole at z = w.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Top.topproof · cited by 9,680
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- WithTopstatement and proof · cited by 3,754
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
- Complex.ofRealproof · cited by 1,654
- LT.lt.ne'proof · cited by 1,417
- sub_zeroproof · cited by 938
Cited by3
Results whose statement or proof uses this declaration.
- Complex.meromorphicNFOn_canonicalFactorproof · cited by 1
- Complex.meromorphicOrderAt_canonicalFactor_ne_topproof · cited by 1
- Complex.divisor_canonicalFactorproof · cited by 0