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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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