Observe the graphs of our approximations to the function you clicked on

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Where: (a) is the function we wish to approximate, (b) is the 1st partial sum, (c) is the 3nd partial sum, (d) is the 7th partial sum, (e) is the 17th partial sum, (f) is the 25th partial sum,(g) the 35nd partial sum, (h) is all of them together.

The coefficients to the Fourier-Bessel Series depend on when BesselJ[0,x]=0 so using the FindRoot command in Mathematica I found the first zero of BesselJ[0,x] (let's call it z[1]) to be 2.404825558. I also used Mathematica to find several more. Here is the next 24 z[n]'s.

Let's look at that in 3-D