BUG: `pandas.Series.eq` doc and result mismatch for fill_value

[rgsl888prabhu]

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• I have confirmed this bug exists on the latest version of pandas.

• (optional) I have confirmed this bug exists on the master branch of pandas.

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Code Sample

>>> import pandas as pd
>>> import numpy as np
>>> pd.Series([np.nan]).eq(pd.Series([np.nan]), fill_value=5.0)
0    False
dtype: bool

Problem description

As per the doc, if fill_value is provided and if the element at a position is missing in both series, then result will also be missing, but as per the result, False is being returned rather than nan.

Expected Output

So, not sure if doc is wrong or output is wrong. So opening this issue just to clarify this and fix appropriate issue.

Output of pd.show_versions()

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.7.3.final.0
python-bits      : 64
OS               : Linux
OS-release       : 5.3.0-26-generic
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.0.1
numpy            : 1.16.4
pytz             : 2019.1
dateutil         : 2.8.0
pip              : 19.1.1
setuptools       : 41.0.1
Cython           : 0.29.12
pytest           : 5.0.1
hypothesis       : None
sphinx           : 2.1.2
blosc            : None
feather          : None
xlsxwriter       : 1.1.8
lxml.etree       : 4.3.4
html5lib         : 1.0.1
pymysql          : None
psycopg2         : None
jinja2           : 2.10.1
IPython          : 7.6.1
pandas_datareader: None
bs4              : 4.7.1
bottleneck       : 1.2.1
fastparquet      : None
gcsfs            : None
lxml.etree       : 4.3.4
matplotlib       : 3.1.0
numexpr          : 2.6.9
odfpy            : None
openpyxl         : 2.6.2
pandas_gbq       : None
pyarrow          : None
pytables         : None
pytest           : 5.0.1
pyxlsb           : None
s3fs             : None
scipy            : 1.3.0
sqlalchemy       : 1.3.5
tables           : 3.5.2
tabulate         : None
xarray           : None
xlrd             : 1.2.0
xlwt             : 1.3.0
xlsxwriter       : 1.1.8
numba            : 0.44.1

[dsaxton]

@rgsl888prabhu This documentation does seem confusing, but I think what it actually means is that the result of filling will be null when both entries are missing rather than the result of the comparison itself (in this case the comparison has a bool dtype, so it actually cannot be null). An internal docstring is a bit more explicit:

If a non-None fill_value is given, replace null entries in left and right with this value, but only in positions where one of left/right is null, not both.

I think this could probably be made more clear in the user-facing docs.