DOC: Updating Series.autocorr docstring
- [ ] closes #xxxx
- [ ] tests added / passed
- [ X ] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

Hello @HubertKl! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/series.py`](https://github.com/HubertKl/pandas/blob/ae96704325233121bba4058cf3b3a6ee89f3161f/pandas/core/series.py) !

 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22787?src=pr&el=h1) Report
> Merging [#22787](https://codecov.io/gh/pandas-dev/pandas/pull/22787?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/bdb7a1603f1e0948ca0cab011987f616e7296167?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/22787/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/22787?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #22787      +/-   ##
==========================================
+ Coverage   92.18%   92.18%   +<.01%     
==========================================
  Files         169      169              
  Lines       50810    50820      +10     
==========================================
+ Hits        46839    46850      +11     
+ Misses       3971     3970       -1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.6% <ø> (ø)` | :arrow_up: |
| #single | `42.38% <ø> (+0.04%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/22787?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `93.74% <ø> (ø)` | :arrow_up: |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `85.82% <0%> (-0.21%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.2% <0%> (ø)` | :arrow_up: |
| [pandas/core/generic.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ2VuZXJpYy5weQ==) | `96.67% <0%> (ø)` | :arrow_up: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `98.1% <0%> (+0.01%)` | :arrow_up: |
| [pandas/core/resample.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvcmVzYW1wbGUucHk=) | `96.97% <0%> (+0.18%)` | :arrow_up: |
| [pandas/core/ops.py](https://codecov.io/gh/pandas-dev/pandas/pull/22787/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvb3BzLnB5) | `97.37% <0%> (+0.29%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22787?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/22787?src=pr&el=footer). Last update [bdb7a16...33dcb33](https://codecov.io/gh/pandas-dev/pandas/pull/22787?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 Thanks @TomAugspurger and @datapythonista for the constructive comments. I taken all of those into account in the last version. do you mind replacing `pearson` by `Pearson` in all the places it's written in the docstring? Unless I made a mistake, I think that I replaced Pearson by pearson in the Third commit.

Edit: sorry I read it too quickly you suggested the other way arond, I got it. Sure! Thanks @HubertKl!