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MathGroup Archive 2007

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Re: Double Integration involving Struve and Neumann functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79703] Re: Double Integration involving Struve and Neumann functions
  • From: chuck009 <dmilioto at comcast.com>
  • Date: Thu, 2 Aug 2007 03:50:17 -0400 (EDT)

Hey Sooraj, that's an interesting function.  Seems to have an indeterminate form when ze=zh but the limit there appears to be zero.  Is this a removable pole?  Look at the two functions:

f1[ze_,zh_]:= (Sqrt[2/Le[[1]]]*Cos[(Pi*ze)/Le[[1]]])^2*
    (Sqrt[2/Lh[[1]]]*Cos[(Pi*zh)/Lh[[1]]])^2*Abs[ze - zh]

f2[ze_,zh_]:=((Pi/2)*(StruveH[1, 2*(Abs[ze - zh]/R)] - 
       BesselY[1, 2*(Abs[ze - zh]/R)]) - 1)]

Then:

f1[x,x] f2[x,x]=0*Infinity

but looks like lim(f1[x,y] f2[x,y],x->y)=0  (not sure though)

So how about just removing the pole by defining the function piecewise (just ignore the prefix for now):

R = 10^3; 

prefix = hbar^2/(2*mu*R^2) - 4*(charge^2/(epsilon*R^2))

f[ze_, zh_] := If[ze == zh, 0, 
   (Sqrt[2/Le[[1]]]*Cos[(Pi*ze)/Le[[1]]])^2*
    (Sqrt[2/Lh[[1]]]*Cos[(Pi*zh)/Lh[[1]]])^2*Abs[ze - zh]*
    ((Pi/2)*(StruveH[1, 2*(Abs[ze - zh]/R)] - 
       BesselY[1, 2*(Abs[ze - zh]/R)]) - 1)]

Plot3D[f[x, y], {x, -25, 25}, {y, -25, 25}]

NIntegrate[f[x, y], {x, -5, 5}, {y, -5, 5}]


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