Rom fourier transfom to fourier series

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SUMMARY

The discussion centers on the relationship between Fourier transform coefficients and Fourier series coefficients. The user seeks a formula to derive Fourier series coefficients (an and bn) from Fourier transform coefficients (Fn), specifically in the form an = X1*(Fn) + X2*(F-n) and bn = X3*(Fn) + X4*(F-n). However, a respondent clarifies that Fourier transforms represent functions rather than coefficients and highlights the fundamental differences between Fourier series, which apply to periodic functions over finite intervals, and Fourier transforms, which apply to non-periodic functions defined over all x.

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brad sue
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HI,
I really need to find a relationship between the coefficients of the Fourier transform coefficients and those for Fourier series, especially how to find Fourier series coefficients from the Fourier transform coefficients.

The teacher talks about this in class but wants us to find the formula by ourselves.

The formula should be like this:
an= X1*(Fn)+X2*(F-n)
bn= X3*(Fn)+X4*(F-n)

Where an and bn are the Fourier series coefficients for cosine and sine respectively. Fn are the Fourier transform coefficients.
Finally X1,X2,X3,X4 are some coefficients( I don't know if they are constant or not)

I could not derive it by myself and did some research with books and online but I have not found something good.

Please can some help me please?
Thank you
B
 
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What do you MEAN by "coefficients" of a Fourier transform? A Fourier transform of a function is a function, not a series or polynomial and does not have "coefficients".

Also I don't see how you can associate a specific Fourier series with a specific Fourier Transform. A Fourier series is always calculated for a function over a finite interval (and periodic with that interval as period) while a Fourier transform is of a function defined for all x (and not, in general, periodic).
 
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