For a given function with a certain finite period, is there only one set of fourier series coefficients [tex]a_n[/tex] and [tex]b_n[/tex]? The reason I ask is, I was doing a problem where it asked for the coefficients for a certain odd function, and then it asked for the coefficients for that same function shifted up by a constant. Are all the [tex]b_n[/tex]'s the same, and [tex]a_0[/tex] just twice the constant? I tried real quick using the definition to see if this came out the same, and it didn't, but I might have made a mistake. Could there be two series for the same function?