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].(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Fourier Series: Can even functions be changed to odd?

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