Update holomorphic_JensenFormula2.lean

Nevanlinna/holomorphic_JensenFormula2.lean

@@ -7,9 +7,21 @@ import Mathlib.Analysis.Analytic.IsolatedZeros
 lemma xx
   {f : ℂ → ℂ}
   {S : Set ℂ}
-  {R : ℝ}
-  (h₁ : DifferentiableOn ℂ f (Metric.ball z₀ R)) :
-  ∃ o : ℂ → ℕ, ∃ F : ℂ → ℂ, ∀ z ∈ (Metric.ball z₀ R), (DifferentiableAt ℂ F z) ∧ (F z ≠ 0) ∧ (f z = F z * ∏ᶠ s ∈ (Metric.ball z₀ R), (z - s) ^ (o s)) := by
+  (h₁S : IsPreconnected S)
+  (h₂S : IsCompact S)
+  (hf : ∀ s ∈ S, AnalyticAt ℂ f s) :
+  ∃ o : ℂ → ℕ, ∃ F : ℂ → ℂ, ∀ z ∈ S, (AnalyticAt ℂ F z) ∧ (F z ≠ 0) ∧ (f z = F z * ∏ᶠ s ∈ S, (z - s) ^ (o s)) := by
+
+  let o : ℂ → ℕ := by
+    intro z
+    if hz : z ∈ S then
+      let A := hf z hz
+      let B := A.order
+
+      exact A.order
+    else
+      exact 0
+
   sorry