DOC: Add .to_xyz to io docs
- [x] closes #41839
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [ ] whatsnew entry

Screenshot below for updated docs

<img width="558" alt="Screen Shot 2021-06-06 at 7 03 23 PM" src="https://user-images.githubusercontent.com/59709552/120942916-e53bf400-c6f9-11eb-96bc-d16dc852f45c.png">

@attack68 For sure. I added the `DataFrame.to_latex` method on a feature branch I'll merge when complete. Looking into the Styler methods now because an import error blocked my original request. @attack68 Added those methods, ready for re-review! > @attack68 Added those methods, ready for re-review!

can you post a render of the page.. i cant generate it or see it here, and just want to check it looks right and has active links? <img width="614" alt="Screen Shot 2021-06-07 at 1 15 28 PM" src="https://user-images.githubusercontent.com/59709552/121061897-7199f580-c792-11eb-91b2-3001965eecda.png">

@attack68 yeah, here's a screenshot which shows a cross section of the three types of changes:
1. Add new section for LaTeX
2. Add DataFrame.to_xyz
3. Add Styler.to_xyz
 @WillAyd The `DataFrame.to_xyz` methods have the DataFrame modifier because they are DataFrame methods and must be done on one. The remaining IO methods aren't done on DataFrames (just `pandas` or `Styler`) so didn't have that prefix. It both lets Sphynx pick up the methods (otherwise they won't be found by the autosummary) and gives users more accurate usage information. You'll notice it is only the output methods that are `Dataframe...` while the input methods are just `pandas...` > There seems to be some CI errors. The docs don't build without errors, I think because the current module is changed in one part of `pandas.io.formats.style` and then `ExcelWriter` is referenced.

@attack68 The docs didn't build without errors when I first tried pre-PR either, but I switched the current module back for ExcelWriter and it is generating properly. I can't kick off the workflows myself, so we'll need to wait until someone else (@WillAyd?) or you (if able) can do so to see if they pass. See screenshot below for ExcelWriter:

<img width="534" alt="Screen Shot 2021-06-08 at 11 14 55 AM" src="https://user-images.githubusercontent.com/59709552/121211781-c39e5200-c84a-11eb-93be-95ce0d85bf6c.png">
 @attack68 I went ahead and resolved the warnings on the page as well. The page is rendering properly for me with no errors. lgtm. can merge on green. > lgtm. can merge on green.

Thanks @jreback will keep an eye on the checks https://github.com/pandas-dev/pandas/pull/41844/checks?check_run_id=2777904153 if you can address > https://github.com/pandas-dev/pandas/pull/41844/checks?check_run_id=2777904153

I can switch that, but `LaTeX` is the proper capitalization for the project (see [LaTeX Website](https://www.latex-project.org/)). Please advise if I should switch it or if there is a way to override that check @jreback  @jreback I just made the change since it is easily revertible. actually this is coming from our validate_rst_ checker cc @MarcoGorelli i think there is a way to ignore it @jreback cc @MarcoGorelli Any update here? moving off 1.3 milestone for now. Looks like there's a new
```
/home/runner/work/pandas/pandas/pandas/io/json/_normalize.py:240:SS04:pandas.io.json.json_normalize:Summary contains heading whitespaces
```

> actually this is coming from our validate_rst_ checker cc @MarcoGorelli i think there is a way to ignore it

Can use [exclude](https://pre-commit.com/#top_level-exclude) to exclude it from a file

----

"LaTex" should probably be "allowlisted" in the check though - @gansel51 if you wanted to contribute that in a separate PR it would be welcome! @jreback @MarcoGorelli @attack68 I removed the deprecated method from the documentation, kicking off a new build could (should?) solve the issue so this PR can merge. I can definitely look into putting LaTeX in the allowlisted next! @attack68 I'm not seeing where the checks are failing and not just failing because of a cancellation, can you point me in the right direction? ```
/home/runner/work/pandas/pandas/doc/source/reference/api/pandas.to_pickle.rst:40: WARNING: Citation [Recbd1b9f7896-1] is not referenced.
```
in https://github.com/pandas-dev/pandas/pull/41844/checks?check_run_id=2800940727 @gansel51 this is ok for 1.3 after its passing. > @attack68 I'm not seeing where the checks are failing and not just failing because of a cancellation, can you point me in the right direction?

isnt this because it should be `DataFrame.to_pickle`. if `pandas.to_pickle` isnt there that will produce the error simonjayhawkins highlighted @attack68 @simonjayhawkins Thanks for pointing it out, I was having trouble isolating the error from the logs. Made that change, will keep an eye on the workflow status. thanks @gansel51  @meeseeksdev backport 1.3.x Something went wrong ... Please have  a look at my logs.