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MathGroup Archive 2011

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Integrate in cylindrical

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122907] Integrate in cylindrical
  • From: Alexander <alexmag25 at hotmail.com>
  • Date: Tue, 15 Nov 2011 05:51:27 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello dear community,

I am running into some difficulty with integration,
When I integrate the following expression in Cartesian coordinates it seems I get result as expected,

h := {hx[x, y, z], hy[x, y, z], hz[x, y, z]} ;
fe = Integrate[
  f[x, y, z] Grad[
    Div[h*DiracDelta[x - a, y - b, z - c], Cartesian[x, y, z]], 
    Cartesian[x, y, z]], {x, -Infinity, Infinity}, {y, -Infinity, 
   Infinity}, {z, -Infinity, Infinity}, 
  Assumptions -> Element[{a, b, c}, Reals]]

However exact same expression in cylindrical coordinates gives me error message Integral does not converge,

Needs["VectorAnalysis`"]
h := {hr[r, \[Phi], z], h\[Phi][r, \[Phi], z], hz[r, \[Phi], z]}; 
fe = Integrate[
  f[r, \[Phi], z] Grad[
    Div[h*r*DiracDelta[r - a, \[Phi] - b, z - c], 
     Cylindrical[r, \[Phi], z]], Cylindrical[r, \[Phi], z]] r, {r, 0, 
   Infinity}, {\[Phi], 0, 2 \[Pi]}, {z, -Infinity, Infinity}, 
  Assumptions -> Element[{a, b, c}, Reals] && r > 0 && 0 < b < 2 \[Pi]]

any hint/help/comment would be greatly appreciated,
thanks. Alex



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