API: Deprecate renamae_axis and reindex_axis
Closes https://github.com/pandas-dev/pandas/issues/17833

Some notes:

- the positional argument for `rename_axis` is `mapper`, which isn't really descriptive of what it does now. Oh well
- Added a TODO in https://github.com/pandas-dev/pandas/compare/master...TomAugspurger:depr-rename_axis?expand=1#diff-492dc2a862db88ec1f1d80589ce8a7d6R92. That will (presumably) break in the future when we remove reindex_axis. I haven't attempted to understand what's going on there yet. Maybe it'll be easy

Hmm, looks like I'll have to give `Panel.reindex` a similar treatment as DataFrame.reindex in #17800  > Hmm, looks like I'll have to give Panel.reindex a similar treatment as DataFrame.reindex in #17800

I really wouldn't bother with that. Panel is deprecated, and IMO there is no need in making Panel's functions consistent. > I really wouldn't bother with that. Panel is deprecated, and IMO there is no need in making Panel's functions consistent.

I wish I had that option :) It seems to be unavoidable though since some generic methods used `reindex_axis` on frame / panel. Changing those to `reindex(foo, axis=axis)` caused failures.

I have it working for Panel. Working on Panel4D now, hopefully not much longer.  We're getting the refactoring of `_validate_axis_style_args` you and Jeff asked for though ;) Another option is to just make a `_reindex_axis` for now that has the actual implementation and is not deprecated, and use that where `reindex_axis` is used now internally, and we can get rid of it once Panel/Panel4D is gone. 
Again, personally I wouldn't loose more time on it than necessary :-)
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=h1) Report
> Merging [#17842](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/727ea20bdb72ff4a5b8380d7f613d4aff058e28a?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/17842/graphs/tree.svg?height=150&width=650&src=pr&token=eZ4WkYLtcO)](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #17842      +/-   ##
==========================================
- Coverage   91.22%   91.21%   -0.02%     
==========================================
  Files         163      163              
  Lines       50014    50033      +19     
==========================================
+ Hits        45627    45637      +10     
- Misses       4387     4396       +9
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.02% <98.38%> (ø)` | :arrow_up: |
| #single | `40.26% <62.9%> (-0.04%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/panel4d.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcGFuZWw0ZC5weQ==) | `100% <100%> (ø)` | :arrow_up: |
| [pandas/core/panel.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcGFuZWwucHk=) | `96.96% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `94.99% <100%> (ø)` | :arrow_up: |
| [pandas/plotting/\_core.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb3JlLnB5) | `82.45% <100%> (ø)` | :arrow_up: |
| [pandas/core/generic.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ2VuZXJpYy5weQ==) | `92.2% <100%> (+0.11%)` | :arrow_up: |
| [pandas/core/sparse/scipy\_sparse.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc3BhcnNlL3NjaXB5X3NwYXJzZS5weQ==) | `97.05% <100%> (ø)` | :arrow_up: |
| [pandas/core/computation/align.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vYWxpZ24ucHk=) | `97.89% <100%> (-0.05%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.75% <100%> (-0.12%)` | :arrow_down: |
| [pandas/io/pytables.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2lvL3B5dGFibGVzLnB5) | `92.79% <100%> (ø)` | :arrow_up: |
| [pandas/core/internals.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzLnB5) | `94.38% <100%> (ø)` | :arrow_up: |
| ... and [5 more](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=footer). Last update [727ea20...c780537](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=h1) Report
> Merging [#17842](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/727ea20bdb72ff4a5b8380d7f613d4aff058e28a?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/17842/graphs/tree.svg?height=150&width=650&token=eZ4WkYLtcO&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #17842      +/-   ##
==========================================
- Coverage   91.22%   91.21%   -0.02%     
==========================================
  Files         163      163              
  Lines       50014    50033      +19     
==========================================
+ Hits        45627    45637      +10     
- Misses       4387     4396       +9
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `89.02% <98.38%> (ø)` | :arrow_up: |
| #single | `40.26% <62.9%> (-0.04%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.75% <100%> (-0.12%)` | :arrow_down: |
| [pandas/io/pytables.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2lvL3B5dGFibGVzLnB5) | `92.79% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexing.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhpbmcucHk=) | `93% <100%> (ø)` | :arrow_up: |
| [pandas/core/internals.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW50ZXJuYWxzLnB5) | `94.38% <100%> (ø)` | :arrow_up: |
| [pandas/core/groupby.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ3JvdXBieS5weQ==) | `91.99% <100%> (ø)` | :arrow_up: |
| [pandas/core/reshape/pivot.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzaGFwZS9waXZvdC5weQ==) | `96.38% <100%> (ø)` | :arrow_up: |
| [pandas/core/panel4d.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcGFuZWw0ZC5weQ==) | `100% <100%> (ø)` | :arrow_up: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `94.99% <100%> (ø)` | :arrow_up: |
| [pandas/core/panel.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcGFuZWwucHk=) | `96.96% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/computation/align.py](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tcHV0YXRpb24vYWxpZ24ucHk=) | `97.89% <100%> (-0.05%)` | :arrow_down: |
| ... and [5 more](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=tree-more) | |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=footer). Last update [727ea20...c780537](https://codecov.io/gh/pandas-dev/pandas/pull/17842?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 https://travis-ci.org/pandas-dev/pandas/jobs/287943551

@TomAugspurger some deprecation warnings still in test_panel I think. can you fix.