Added an edge case handler and a test case for Series.first("#M")

doc/source/whatsnew/v2.1.0.rst

@@ -260,6 +260,7 @@ Styler
 
 Other
 ^^^^^
+- Bug in :func:`Series.first` ``first`` not returning all the timestamps of the last day of a month when parameter is month-based (:issue:`51285`)
 - Bug in :func:`assert_almost_equal` now throwing assertion error for two unequal sets (:issue:`51727`)
 - Bug in :meth:`Series.memory_usage` when ``deep=True`` throw an error with Series of objects and the returned value is incorrect, as it does not take into account GC corrections (:issue:`51858`)
 

pandas/core/generic.py

@@ -188,6 +188,10 @@
     DataFrameRenderer,
 )
 from pandas.io.formats.printing import pprint_thing
+from pandas.tseries.offsets import (
+    Day,
+    MonthEnd,
+)
 
 if TYPE_CHECKING:
     from pandas._libs.tslibs import BaseOffset
@@ -9074,6 +9078,14 @@ def first(self, offset) -> Self:
             end = self.index.searchsorted(end_date, side="left")
             return self.iloc[:end]
 
+        # if original offset is "#M", MonthEnd only includes
+        # the first timestamp of the last day of the month
+        # however, first() should return the rest timestamps of the day as well
+        if isinstance(offset, MonthEnd):
+            end_date = end_date.date() + Day()
+            end = self.index.searchsorted(end_date, side="left")
+            return self.iloc[:end]
+
         return self.loc[:end]
 
     @final

pandas/tests/frame/methods/test_first_and_last.py

@@ -95,3 +95,15 @@ def test_empty_not_input(self, func):
         result = getattr(df, func)(offset=1)
         tm.assert_frame_equal(df, result)
         assert df is not result
+
+    @pytest.mark.parametrize("start, periods, freq", [("2018-02-01", 3000, "1H")])
+    def test_first_with_offsets_in_month(self, frame_or_series, start, periods, freq):
+        # GH#51285
+        x = frame_or_series(
+            [1] * periods, index=bdate_range(start, periods=periods, freq=freq)
+        )
+        result = x.first("1M")
+        expected = frame_or_series(
+            [1] * 672, index=bdate_range(start, periods=672, freq=freq)
+        )
+        tm.assert_equal(result, expected)