Fourier series in Mathematica

[Equations in this post may not look right (or appear at all) in your RSS reader. Go to the original article to see them rendered properly.] After my last post—the one about using Fourier series—I started thinking about how to use Mathematica to develop Fourier series.1 I could, of course, use the Integrate function to determine the Fourier coefficients, but Mathematica has other functions that can do the job directly once you understand how they work. Mathematica has several Fourier functions, but I’m going to stick with the ones associated with sine series, FourierSinCoefficient and FourierSinSeries. They’re meant to be easy to use, and they are, but you need to know how they’re defined. The coefficients used in both of these functions are defined this way: fn=2π∫0πf(x)sin⁡nxdx This doesn’t match up exactly with the definition I used for getting the Fourier coefficients of a loading function, q(x): qn=2L∫0Lq(x)sin⁡nπxLdx To use the Mathematica functions to get the qn, we have to do…