CLN: Remove PeriodIndex.tz_convert, tz_localize
- [x] closes #21781 
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`

- Removed PeriodIndex.tz_convert and PeriodIndex.tz_localize from PeriodIndex.
- Removed references to those methods in test_tz_convert_and_localize within test_timeseries
- Removed methods from the PeriodIndex class doc and updated whatsnew

test_tz_convert_and_localize also contains a TODO referencing changing the test to use PeriodIndex for a timezone test, which if it is never gaining timezone info should probably be removed. I just wanted to check that this was a good idea before doing it.

There's a linting problem in the test file.

Other than that, assuming there's a consensus about removing these, LGTM. # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21935?src=pr&el=h1) Report
> Merging [#21935](https://codecov.io/gh/pandas-dev/pandas/pull/21935?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/272bbdc72fa2d32d7019bb76ab91817eb5afeaf5?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/21935/graphs/tree.svg?width=650&height=150&src=pr&token=eZ4WkYLtcO)](https://codecov.io/gh/pandas-dev/pandas/pull/21935?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #21935      +/-   ##
==========================================
+ Coverage   91.96%   91.96%   +<.01%     
==========================================
  Files         166      166              
  Lines       50323    50329       +6     
==========================================
+ Hits        46281    46287       +6     
  Misses       4042     4042
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.36% <ø> (ø)` | :arrow_up: |
| #single | `42.23% <ø> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/21935?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9wZXJpb2QucHk=) | `93.17% <ø> (-0.04%)` | :arrow_down: |
| [pandas/core/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tbW9uLnB5) | `92.08% <0%> (-0.12%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.19% <0%> (ø)` | :arrow_up: |
| [pandas/core/generic.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ2VuZXJpYy5weQ==) | `96.46% <0%> (ø)` | :arrow_up: |
| [pandas/core/panel.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcGFuZWwucHk=) | `97.44% <0%> (ø)` | :arrow_up: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `94.11% <0%> (ø)` | :arrow_up: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.35% <0%> (ø)` | :arrow_up: |
| [pandas/core/reshape/concat.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzaGFwZS9jb25jYXQucHk=) | `97.6% <0%> (ø)` | :arrow_up: |
| [pandas/core/sparse/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc3BhcnNlL2ZyYW1lLnB5) | `94.79% <0%> (+0.01%)` | :arrow_up: |
| [pandas/core/sparse/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc3BhcnNlL3Nlcmllcy5weQ==) | `95.22% <0%> (+0.01%)` | :arrow_up: |
| ... and [1 more](https://codecov.io/gh/pandas-dev/pandas/pull/21935/diff?src=pr&el=tree-more) | |

------

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> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21935?src=pr&el=footer). Last update [272bbdc...f46f848](https://codecov.io/gh/pandas-dev/pandas/pull/21935?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 @jreback Everything look good? @jquinon :  Everyone seems happy, so yes, indeed!  Thanks!