Follow these steps to create a Cartesian product:

1. Construct two Series that have indexes that are different but contain some of the same values:

>>> s1 = pd.Series(index=list('aaab'), data=np.arange(4))
>>> s1
a    0
a    1
a    2
b    3
dtype: int64

>>> s2 = pd.Series(index=list('cababb'), data=np.arange(6))
>>> s2
c    0
a    1
b    2
a    3
b    4
b    5
dtype: int64

2. Add the two Series together to produce a Cartesian product:

>>> s1 + s2
a    1.0
a    3.0
a    2.0
a    4.0
a    3.0
a    5.0
b    5.0
b    7.0
b    8.0
c    NaN
dtype: float64