Fourier Series No.2: Evaluating Function g(x)

In summary, a Fourier series is a mathematical representation of a periodic function using an infinite sum of sine and cosine functions. It is evaluated by finding the coefficients through integration and can be used to approximate functions in various applications. However, not all functions can be represented by a Fourier series and there are limitations, such as the need for an infinite number of terms to accurately represent some functions.
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asi123
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Fourier series no.2 :)

Homework Statement



Hey guys.
So I have this function f(x) between -pi and pi.
I found the Fourier series for it.
Now I need to find the Fourier series for g(x). The problem is, I'm not sure about g(x), is it correct what I did?
Thanks in advance.


Homework Equations





The Attempt at a Solution

 

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Can't tell what you did, since the attachment is still pending approval.
 

FAQ: Fourier Series No.2: Evaluating Function g(x)

What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as an infinite sum of sine and cosine functions. It is named after the French mathematician Joseph Fourier who first proposed it in the early 19th century.

How is a Fourier series evaluated?

A Fourier series is evaluated by finding the coefficients of the sine and cosine terms through integration and then plugging them into the formula for a Fourier series. This results in a representation of the original function in terms of trigonometric functions.

What is the purpose of evaluating a Fourier series?

Evaluating a Fourier series allows us to approximate a periodic function with a simpler sum of trigonometric functions. This can be useful in various applications such as signal processing, image compression, and solving differential equations.

Can any function be represented by a Fourier series?

No, not every function can be represented by a Fourier series. The function must be periodic and satisfy certain conditions for the series to converge. Additionally, the function must be single-valued and continuous with only a finite number of discontinuities.

Are there any limitations to using Fourier series to approximate a function?

One limitation is that the Fourier series may not converge to the exact function, but rather to a close approximation. This can be improved by using more terms in the series. Additionally, some functions may require an infinite number of terms in the series to accurately represent them.

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