rom fourier transfom to fourier series

brad sue

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

HallsofIvy

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).