Even and odd expansion of a function in [-2L,2L] Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Fourier series odd and even functionsExtending a function to become odd or even?Fourier series representation of even and odd functionsWhy does specifying an interval for a function make the function odd or even?If the fourier integral of a function exists, is it always equal to the fourier cosine integral of that function?Fourier expansion of even extension of cosine squareBasis of Even and Odd FunctionsEven and odd functions with Fourier seriesDifferences in the Drawings of Fourier SeriesWhat's the difference between Fourier Cosine and Sine Series besides the periodic function?
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Even and odd expansion of a function in [-2L,2L]
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Fourier series odd and even functionsExtending a function to become odd or even?Fourier series representation of even and odd functionsWhy does specifying an interval for a function make the function odd or even?If the fourier integral of a function exists, is it always equal to the fourier cosine integral of that function?Fourier expansion of even extension of cosine squareBasis of Even and Odd FunctionsEven and odd functions with Fourier seriesDifferences in the Drawings of Fourier SeriesWhat's the difference between Fourier Cosine and Sine Series besides the periodic function?
$begingroup$
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.
fourier-series
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
$endgroup$
add a comment |
$begingroup$
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.
fourier-series
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
$endgroup$
$begingroup$
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.
$endgroup$
– Thomas Andrews
Apr 2 at 17:52
$begingroup$
Extension may the correct term I am looking for here.
$endgroup$
– MathsRookie
Apr 2 at 17:55
$begingroup$
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?
$endgroup$
– Pink Panther
Apr 2 at 19:03
$begingroup$
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?
$endgroup$
– MathsRookie
Apr 2 at 19:28
add a comment |
$begingroup$
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.
fourier-series
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
$endgroup$
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.
fourier-series
fourier-series
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
asked Apr 2 at 17:47
MathsRookieMathsRookie
1237
1237
$begingroup$
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.
$endgroup$
– Thomas Andrews
Apr 2 at 17:52
$begingroup$
Extension may the correct term I am looking for here.
$endgroup$
– MathsRookie
Apr 2 at 17:55
$begingroup$
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?
$endgroup$
– Pink Panther
Apr 2 at 19:03
$begingroup$
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?
$endgroup$
– MathsRookie
Apr 2 at 19:28
add a comment |
$begingroup$
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.
$endgroup$
– Thomas Andrews
Apr 2 at 17:52
$begingroup$
Extension may the correct term I am looking for here.
$endgroup$
– MathsRookie
Apr 2 at 17:55
$begingroup$
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?
$endgroup$
– Pink Panther
Apr 2 at 19:03
$begingroup$
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?
$endgroup$
– MathsRookie
Apr 2 at 19:28
$begingroup$
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.
$endgroup$
– Thomas Andrews
Apr 2 at 17:52
$begingroup$
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.
$endgroup$
– Thomas Andrews
Apr 2 at 17:52
$begingroup$
Extension may the correct term I am looking for here.
$endgroup$
– MathsRookie
Apr 2 at 17:55
$begingroup$
Extension may the correct term I am looking for here.
$endgroup$
– MathsRookie
Apr 2 at 17:55
$begingroup$
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?
$endgroup$
– Pink Panther
Apr 2 at 19:03
$begingroup$
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?
$endgroup$
– Pink Panther
Apr 2 at 19:03
$begingroup$
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?
$endgroup$
– MathsRookie
Apr 2 at 19:28
$begingroup$
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?
$endgroup$
– MathsRookie
Apr 2 at 19:28
add a comment |
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$begingroup$
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.
$endgroup$
– Thomas Andrews
Apr 2 at 17:52
$begingroup$
Extension may the correct term I am looking for here.
$endgroup$
– MathsRookie
Apr 2 at 17:55
$begingroup$
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?
$endgroup$
– Pink Panther
Apr 2 at 19:03
$begingroup$
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?
$endgroup$
– MathsRookie
Apr 2 at 19:28