What is the Fourier-series for a function with a random period?

[Niles]

Homework Statement

I have the Fourier-series for the function:

f(x) = x for -Pi < x < Pi.

I know wish to find the Fourier-series for the function:

g(x) = x for -p < x < p,

where p is a random period.

The Attempt at a Solution

Ok, the obvious thing here is to use the result from f(x). If thought that if I define f(p*x/Pi) = g(x) = f(y), then I just insert x=y*Pi/p. But in the result of this exercise, they have an additional p/Pi in front of the sum. Where does this come from?

 

[Niles]

I solved it - just substitute, and then you have a regular equation.. remember to make the substitution in the limit as well!