pandas two dataframe cross join [duplicate]

Create a common 'key' to cross join the two:

df1['key'] = 0
df2['key'] = 0

df1.merge(df2, on='key', how='outer')

For the cross product, see this question.

Essentially, you have to do a normal merge but give every row the same key to join on, so that every row is joined to each other across the frames.

You can then add a column to the new frame by applying your function:

new_df = pd.merge(df1, df2, on=key)
new_df.new_col = new_df.apply(lambda row: myfunc(row['A_x'], row['A_y']), axis=1)

axis=1 forces .apply to work across the rows. 'A_x' and 'A_y' will be the default column names in the resulting frame if the merged frames share a column like in your example above.