First off sorry to make another post on てくる, but I am really having troubles
understanding this construction. I have consulted various resources and have
read other similar questions on this website but I can't seem to get it.

My resources (the basic dictionary of Japanese grammar) tell me the following:

来る - an aux verb which indicates the beginning of some process or continuation
of some action up to a current point in time.

So when we look at this sentence:

寒くなってきた。

I would draw upon the above and envision that the weather has begun getting
cold and is still now getting cold. However, sometimes I see similar sentences
translated as "It's gotten cold." To me there is a difference between "getting
cold" and "has gotten cold". The former seems like a change still in progress
and the latter seems like a complete change.

If it is indeed the latter, what would be the difference between just saying
寒くなった。or, 前より寒くなった。?

Then we move on to a sentence like this, which gets this meaning -
"continuation of some action up to a current point in time."

3年間日本語を勉強してきました。

I understand this as, "I have studied Japanese for 3 years", but in this usage
I am struggling to understand it's usage over just saying something like
"3年間日本語を勉強しています。"

And finally, where does てきている come into this? I've had troubles finding a
source on this...
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2020-04-29T20:00:46.770
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2020-04-30T07:25:33.347
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question
nuances
てきた in terms of aspect?
As long as durative verbs like ３年勉強する are concerned, ３年勉強してきた can mean that
you studied for 3 years and came back (it's not sure when you started), or
that you have studied for 3 years up until today, while ３年勉強している means that
you have studied for 3 years (not sure when you started).

So, unless you have stopped it beforehand, they are semantically the same. If
any, してきた has sense of accumulation.

On the other hand, instantaneous verbs can be combined with ている to stand for
perfect aspect like 行っている can mean that you have been somewhere, but not with
てきた because てくる and ていく themselves are a durative verb. 行ってきた only means that
you went somewhere and came back.

してきている can express

  * perfect aspect of doing something and coming back
  * that you have experience of doing something repetitively for a certain period. (勝っている: I have earned a victory 勝ってきている: I have earned victories)
  * that a gradual change of something is on-going. (てきた doesn't refer to the change from now on.)
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answer