If I were to find the general Fourier Series expression for a function that is defined for example in the [-pie, pie] or [-2pi, 2pi] intervals. What is my L? Do I directly take L as pi or 2pi, or do I have to divide by 2 such that 2L = pi, therefore, L = pi/2?    I have seen so many examples online where the period was given as f(t+2) so the solution was 2L = 2, therefore, L = 1.. But I have also seen questions like f(t) = -5t when 0< t <1 10-5t 1< t <2 What is my L going to be in this case?  Is it going to be different when I'm dealing with Odd/Even functions?

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If I were to find the general Fourier Series expression for a function that is defined for example in the [-pie, pie] or [-2pi, 2pi] intervals. What is my L? Do I directly take L as pi or 2pi, or do I have to divide by 2 such that 2L = pi, therefore, L = pi/2? 

 

I have seen so many examples online where the period was given as f(t+2) so the solution was 2L = 2, therefore, L = 1.. But I have also seen questions like

f(t) = -5t  when 0< t <1

         10-5t      1< t <2

What is my L going to be in this case? 

Is it going to be different when I'm dealing with Odd/Even functions? 

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