# Fourier Series question

1. Sep 17, 2011

### nlsherrill

So im in PDE's and we are deriving certain fourier series for periodic functions. I have notice that the solution manual to the book Partial Differential Equations with Fourier Series and Boundary Value Problems by Asmar tends to emphasize infinite sums frequently with "n" equal to 2k for even and 2k+1 for odd. What does it matter if you sum over the odd or even values of a series when you are summing from 1 to infinity anyway? I just want to get my answers to match the solutions and I don't see why its necessary to have this extra step involved.