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This could be very obvious and I am just not understanding very well.

I'm a little bit confused and can't seem to find the answer I am looking for even though it is probably simple. Looking online I can see plenty of examples of of extending (not sure this is the right term) a function to the interval $[-L,0]$ but not similar to my example below:

Say for example:

I consider the function $ f(x) = x^4$ in $[0,L]$ and am then asked to determine the even and odd expansions of $f(x)$ in $[-2L,2L]$.

How would I go about doing this compared to the interval $[-L,L]$? This example then leads into constructing sine and cosine fourier series in the interval $[-L,L]$ but I think I can do this part.

Apologies if my question is worded poorly and if you can help me work through this example it would be appreciated.

MathsRookie
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  • Better to be clear what you mean by "expansion." I'm guessing from the tag, but tags are rarely for reading the question, more for aiding people search questions. – Thomas Andrews Apr 02 '19 at 17:52
  • Extension may the correct term I am looking for here. – MathsRookie Apr 02 '19 at 17:55
  • I feel like the task is stated in a confusing way. Could you elaborate what "expansion" means here? Like what should the "expansion" look like? – Pink Panther Apr 02 '19 at 19:03
  • I feel like this may be what is confusing me as such as the example/question I have been given is stated as I have done so in my post. I am wondering if my professor has used the correct terminology and I feel like expansion is more of a correct term? For the example above I would need to construct the odd/even "expansion" of f to $[-2L,2L]$. I hope this makes sense? – MathsRookie Apr 02 '19 at 19:28

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