diff --git a/docs/api-reference/dataframe.md b/docs/api-reference/dataframe.md
index 676f64076..b251b2a50 100644
--- a/docs/api-reference/dataframe.md
+++ b/docs/api-reference/dataframe.md
@@ -4,6 +4,7 @@
     handler: python
     options:
       members:
+        - __arrow_c_stream__
         - __getitem__
         - clone
         - collect_schema
diff --git a/docs/api-reference/series.md b/docs/api-reference/series.md
index 7b7f62b8a..f9cc2e6bb 100644
--- a/docs/api-reference/series.md
+++ b/docs/api-reference/series.md
@@ -4,6 +4,8 @@
     handler: python
     options:
       members:
+        - __arrow_c_stream__
+        - __getitem__
         - abs
         - alias
         - all
diff --git a/utils/check_api_reference.py b/utils/check_api_reference.py
index 68c980086..f6e5303c4 100644
--- a/utils/check_api_reference.py
+++ b/utils/check_api_reference.py
@@ -45,13 +45,13 @@
 documented = [
     remove_prefix(i, "        - ")
     for i in content.splitlines()
-    if i.startswith("        - ")
+    if i.startswith("        - ") and not i.startswith("        - _")
 ]
 if missing := set(top_level_functions).difference(documented):
     print("DataFrame: not documented")  # noqa: T201
     print(missing)  # noqa: T201
     ret = 1
-if extra := set(documented).difference(top_level_functions).difference({"__getitem__"}):
+if extra := set(documented).difference(top_level_functions):
     print("DataFrame: outdated")  # noqa: T201
     print(extra)  # noqa: T201
     ret = 1
@@ -87,7 +87,7 @@
 documented = [
     remove_prefix(i, "        - ")
     for i in content.splitlines()
-    if i.startswith("        - ")
+    if i.startswith("        - ") and not i.startswith("        - _")
 ]
 if (
     missing := set(top_level_functions)