The expressions for the coefficients of a fourier series are valid for all integers [0;n]. Though sometimes when I evaluate the fourier series of an even function (composed only of cosines) I get an expression for the r'th coefficient, which has r in the demoninator. It could be for instance: ar = (-1)r/(rπ) Since division by zero is not allowed this expression doesn't hold for the r=0, i.e. the first coefficient in the sum of cosines. What is that, that is not reversible, in the proces of solving the integral for the r'th coefficient? Because the integral expression clearly works for all r.