BUG: Series.agg() with axis=1 inconsistent with Series.groupby.agg with axis=1

[kwhkim]

Pandas version checks

• I have checked that this issue has not already been reported.

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

• I have confirmed this bug exists on the main branch of pandas.

I must admit there were similar complaints before, here I present my analysis and solution. (ex. API: Signature of UDF methods, Higher Order Methods API)

Reproducible Example

import pandas as pd
import numpy as np
dat = pd.DataFrame({'color':['A', 'A', 'E', 'E', 'J'],
                    'carat':[0.23, 0.21, 0.23, 0.29, 0.31],
                    'x':[3.95, 3.89, 4.05, 4.20, 4.34]},
                  index = [1,2,3,4,5])

dat['carat'].agg(np.mean)
## 0.254
dat['carat'].agg(np.mean, axis=0)
## 0.254
dat['carat'].agg('mean')
## 0.254
dat['carat'].agg(lambda x: np.mean(x))
## 1    0.23
## 2    0.21
## 3    0.23
## 4    0.29
## 5    0.31
## Name: carat, dtype: float64
dat['carat'].agg(lambda x, axis: np.mean(x, axis=axis), axis=0)
## TypeError: <lambda>() missing 1 required positional argument: 'axis'


Compare the result above with the result below

```python
dat['carat'].groupby(dat['color']).agg(np.mean), 
dat['carat'].groupby(dat['color']).agg(np.mean, axis=0), 
dat['carat'].groupby(dat['color']).agg('mean'), 
dat['carat'].groupby(dat['color']).agg(lambda x: np.mean(x)), 
dat['carat'].groupby(dat['color']).agg(lambda x, axis: np.mean(x, axis=axis), axis=0)
## <all the same here>
## color
## A    0.22
## E    0.26
## J    0.31
## Name: carat, dtype: float64,
##
##

Call it bug or inconsistency or poor design?

Issue Description

Basically, in consistency's term, pd.Series.agg() and pd.Series.groupby().agg() should act the same way.

Anyway as I read the the code(the code is in the bottom), I found parameter axis for Series.aggregate() seems useless(or am I missing something here?)

Even if it really needs a named paramter, it'd better be named something like _axis_ to avoid conflicting names with
functions to apply. For example np.mean() has a parameter named axis= and user might name a parameter axis (for example, lambda x, axis: np.mean(x, axis=axis)).

As far as I know, we do not need axis=0 and self._get_axis_number(axis) for Series at least(DataFrame has similar signature, and I think it should be renamed to something like _axis_ or _axis or __axis__).

So I propose deleting axis parameter from Series.aggregate and renaming axis to _axis for DataFrame.aggreate.

    def aggregate(self, func=None, axis=0, *args, **kwargs):
        # Validate the axis parameter
        self._get_axis_number(axis)

        # if func is None, will switch to user-provided "named aggregation" kwargs
        if func is None:
            func = dict(kwargs.items())

        op = SeriesApply(self, func, convert_dtype=False, args=args, kwargs=kwargs)
        result = op.agg()
        return result

Expected Behavior

dat['carat'].groupby(dat['color']).agg(lambda x: np.mean(x)) and
dat['carat']..agg(lambda x: np.mean(x)) works similarly

Installed Versions

INSTALLED VERSIONS

commit : 06d2301
python : 3.8.12.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19044
machine : AMD64
processor : Intel64 Family 6 Model 94 Stepping 3, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : Korean_Korea.949

pandas : 1.4.1
numpy : 1.22.2
pytz : 2021.3
dateutil : 2.8.2
pip : 22.0.3
setuptools : 60.9.3
Cython : 0.29.28
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.8.0
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 8.0.1
pandas_datareader: None
bs4 : 4.10.0
bottleneck : None
fastparquet : None
fsspec : 2022.02.0
gcsfs : None
matplotlib : 3.5.1
numba : None
numexpr : 2.8.1
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : 1.0.9
s3fs : None
scipy : 1.8.0
sqlalchemy : None
tables : 3.7.0
tabulate : None
xarray : None
xlrd : 2.0.1
xlwt : None
zstandard : None

[jackgoldsmith4]

I think docs clarifying the axis parameter (#47109) might clear up some of the confusion here