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I want to plot solution of some physics problem that I solved (for r between 1 and 2 and for f between 0 and Pi). I tried it myself but since I am beginner in using Wolfram Mathematica I have not managed to do it.

enter image description here

I tried using this:

Plot3D[
  Sum[
    (((1/2)*BesselJ[l, (BesselJZero[l, n])/2]*Sin[lPi/2] BesselJ[l, (BesselJZero[l, n])*(r - 1)]* Sin[lf])/((BesselJZero[l, n])*(BesselJZero[l, n])*(Pi/4) BesselJ[l + 1, (BesselJZero[l, n])])), 
    {l, 1, Infinity}, {n, 1, Infinity}
  ] // Evaluate, 
 {r, 1, 2}, {f, 0, Pi}
]

I also tried to evaluate the sum for the specific point(r = 1.3 and f = Pi/4) and got this: enter image description here

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1 Answer 1

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Use partial sum.

Clear[r, f, N1]

g[r_, f_, N1_] := 
 Sum[(((1/2)*BesselJ[l, (BesselJZero[l, n])/2]*
      Sin[l*Pi/2] BesselJ[l, (BesselJZero[l, n])*(r - 1)]*
      Sin[l*f])/((BesselJZero[l, n])*(BesselJZero[l, n])*(Pi/
        4) BesselJ[l + 1, (BesselJZero[l, n])])), {l, 1, N1}, {n, 1, 
   N1}]

Plot3D[g[r, f, 2], {r, 1, 2}, {f, 0, Pi}]

enter image description here

Now experiment with N1 for large values.

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