diff --git a/doc/source/timedeltas.rst b/doc/source/timedeltas.rst
index 745810704f665..e602e45784f4a 100644
--- a/doc/source/timedeltas.rst
+++ b/doc/source/timedeltas.rst
@@ -363,6 +363,13 @@ or ``np.timedelta64`` objects. Passing ``np.nan/pd.NaT/nat`` will represent miss
    pd.TimedeltaIndex(['1 days', '1 days, 00:00:05',
                      np.timedelta64(2,'D'), datetime.timedelta(days=2,seconds=2)])
 
+The string 'infer' can be passed in order to set the frequency of the index as the
+inferred frequency upon creation:
+
+.. ipython:: python
+
+   pd.TimedeltaIndex(['0 days', '10 days', '20 days'], freq='infer')
+
 Generating Ranges of Time Deltas
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
diff --git a/doc/source/timeseries.rst b/doc/source/timeseries.rst
index 1b0cf86995a39..5262eedc23baa 100644
--- a/doc/source/timeseries.rst
+++ b/doc/source/timeseries.rst
@@ -185,6 +185,19 @@ options like ``dayfirst`` or ``format``, so use ``to_datetime`` if these are req
 
     pd.Timestamp('2010/11/12')
 
+You can also use the ``DatetimeIndex`` constructor directly:
+
+.. ipython:: python
+
+    pd.DatetimeIndex(['2018-01-01', '2018-01-03', '2018-01-05'])
+
+The string 'infer' can be passed in order to set the frequency of the index as the
+inferred frequency upon creation:
+
+.. ipython:: python
+
+    pd.DatetimeIndex(['2018-01-01', '2018-01-03', '2018-01-05'], freq='infer')
+
 Providing a Format Argument
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 83950f1d71633..963eb6dc053bf 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -186,7 +186,10 @@ class DatetimeIndex(DatelikeOps, TimelikeOps, DatetimeIndexOpsMixin,
     copy  : bool
         Make a copy of input ndarray
     freq : string or pandas offset object, optional
-        One of pandas date offset strings or corresponding objects
+        One of pandas date offset strings or corresponding objects. The string
+        'infer' can be passed in order to set the frequency of the index as the
+        inferred frequency upon creation
+
     start : starting value, datetime-like, optional
         If data is None, start is used as the start point in generating regular
         timestamp data.
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 9707d19953418..e90e1264638b0 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -107,7 +107,10 @@ class TimedeltaIndex(DatetimeIndexOpsMixin, TimelikeOps, Int64Index):
         Optional timedelta-like data to construct index with
     unit: unit of the arg (D,h,m,s,ms,us,ns) denote the unit, optional
         which is an integer/float number
-    freq: a frequency for the index, optional
+    freq : string or pandas offset object, optional
+        One of pandas date offset strings or corresponding objects. The string
+        'infer' can be passed in order to set the frequency of the index as the
+        inferred frequency upon creation
     copy  : bool
         Make a copy of input ndarray
     start : starting value, timedelta-like, optional