       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[]]*Cos[(Pi*ze)/Le[]])^2*
(Sqrt[2/Lh[]]*Cos[(Pi*zh)/Lh[]])^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[]]*Cos[(Pi*ze)/Le[]])^2*
(Sqrt[2/Lh[]]*Cos[(Pi*zh)/Lh[]])^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}]

```

• Prev by Date: Re: Function definition within a module (about variable renaming)
• Next by Date: Re: Dot or Inner ... but not quite
• Previous by thread: Re: Double Integration involving Struve and Neumann functions
• Next by thread: Re: FindRoot[] with mixed complex and real variables?