When creating a Fourier series for a function [itex]f(x)[/itex], I consider whether the function is odd or even first. Yet, often these functions are in the positive region [itex] [0, L] [/itex]. Since [itex]f(x)[/itex] is only defined in this region, can I change the function to get a desired parity? By example, my concern originated with the function [itex]f(x) = x \sin x[/itex]. This is an even function, but I could modify the function as [itex]f(x) = |x| \sin x [/itex] to make it odd while retaining the desired information in [itex] [0, L] [/itex]. Can this be done? And are there problems with doing this? Thanks.