Theorems · Theorem · complex analysis
ValueDistribution.circleIntegrable_log_meromorphicTrailingCoeffAt
∀ {f : ℂ → ℂ}, CircleIntegrable (fun a => Real.log ‖meromorphicTrailingCoeffAt (fun x => f x - a) 0‖) 0 1Circle integrability of the term fun a ↦ log ‖meromorphicTrailingCoeffAt (f · - a) 0‖ that
appears in Cartan's formula.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Norm.normstatement and proof · cited by 5,413
- WithTopproof · cited by 3,754
- absproof · cited by 1,814
- Real.logstatement and proof · cited by 939
- sub_zeroproof · cited by 938
- Metric.sphereproof · cited by 371
- norm_zeroproof · cited by 366
- meromorphicOrderAtproof · cited by 180
- lt_trichotomyproof · cited by 178
- MeromorphicAtproof · cited by 160
Cited by2
Results whose statement or proof uses this declaration.
- ValueDistribution.characteristic_top_eq_circleAverage_add_circleAverageproof · cited by 3
- ValueDistribution.circleIntegrable_logCountingproof · cited by 2