DOC: clean up DataFrame.ewm

[MarcoGorelli]

A few issues I've noticed:

1. It says

When adjust is False, weighted averages are calculated recursively as:

weighted_average[0] = arg[0]; weighted_average[i] = (1-alpha)*weighted_average[i-1] + alpha*arg[i].

but arg isn't defined

2. The phrase "When adjust is False, weighted averages are calculated recursively as:" appears as bold, but I don't think this was the intention

\text{for} halflife > 0

should be

\text{for } halflife > 0

4. In the "notes" section, alpha is used, while in the description of the parameters, it's

:math:`\alpha` 

5. The respective doc for Series could be updated, as it says

axis{0 or ‘index’, 1 or ‘columns’}, default 0

[avimiller]

Me and a few other Data Science Majors I am working with are interested in looking into this as a first contribution if that's okay.

[MarcoGorelli]

@avimiller sure, pull requests welcome. Check out the contributing guide for how to get started

[avimiller]

@MarcoGorelli sounds good, thank you.

[klakho0400]

hey @MarcoGorelli can you pls explain me what can i do for the 1.
in 3. should be \text{ for } halflife > 0
in 4.do all alphas in notes need to be replaced by :math:\alpha?
in 5. does it needs to be changed like this axis{0 or ‘rows', 1 or ‘columns’}, default 0

[MarcoGorelli]

To clarify:

1. figure out what the arg in the formula refers to, and make it clear

2. the ones in the "notes" section, yes

3. for Series, there is no notion of 'columns', so axis would have to refer to only the rows (see other methods such as set_axis to see how this differs between the two)

[MarcoGorelli]

@avimiller if you're working on this, can you comment 'take' to let others know? Else, it looks like @klakho0400 is also interested

[mehersaipreetam]

take

[MarcoGorelli]

Closed in #32231