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How to do expansion as power series of any random function?

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How to do expansion as power series of any random function??

The template doesn't really apply because this is a general question rather than a specific problem.

If I am given some function, how do I expand it as a power series? For the past two semesters of my physics degree, I have been seeing this done repeatedly. Yet I still don't know how to do it, really. It isn't taught anywhere! The textbooks we use assume that we know how it works, and also that apparently it's quite simple. But none of our required classes specifically go over this topic; supposedly it was taught way back in Calc 2 but that was years ago, in high school, and as far as I remember it wasn't really taught from this angle anyway... the focus was more about how to work with and what to do with series when you have them rather than how to create a series when you don't have one.

So I want to be like those authors in the textbooks: I'm given some function, bam, I spit out the equivalent power series. How do I do that? Any source on the internet where this is explained clearly and thoroughly? (Obviously wikipedia is not helpful at all...)

Actually, the specific problem I was trying to deal with is this: expand sqrt(1 + epsilon) as a power series.

Thanks a lot
 
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