BUG: Fix calling groupBy(...).apply(func) on an empty dataframe invokes func

pandas/core/groupby/ops.py

@@ -787,15 +787,14 @@ def apply(
             if not mutated and not _is_indexed_like(res, group_axes, axis):
                 mutated = True
             result_values.append(res)
-
         # getattr pattern for __name__ is needed for functools.partial objects
-        if len(group_keys) == 0 and getattr(f, "__name__", None) not in [
-            "idxmin",
-            "idxmax",
-            "nanargmin",
-            "nanargmax",
+        if len(group_keys) == 0 and getattr(f, "__name__", None) in [
+            "mad",
+            "skew",
+            "sum",
+            "prod",
         ]:
-            # If group_keys is empty, then no function calls have been made,
+            #  If group_keys is empty, then no function calls have been made,
             #  so we will not have raised even if this is an invalid dtype.
             #  So do one dummy call here to raise appropriate TypeError.
             f(data.iloc[:0])

pandas/tests/groupby/test_apply.py

@@ -1331,3 +1331,19 @@ def test_result_name_when_one_group(name):
     expected = Series([1, 2], name=name)
 
     tm.assert_series_equal(result, expected)
+
+
+def test_empty_df():
+    # GH 47985
+    empty_df = DataFrame({"a": [], "b": []})
+
+    # Both operations should return an empty series instead of IndexError for apply UDF
+    result1 = empty_df.groupby("a", group_keys=True).b.apply(lambda x: x.values[-1])
+    result2 = empty_df.groupby("a", group_keys=True).b.agg("sum")
+
+    expected = Series(
+        [], name="b", dtype="float64", index=Index([], dtype="float64", name="a")
+    )
+
+    tm.assert_series_equal(result1, expected)
+    tm.assert_series_equal(result2, expected)