       Integration of Singular function

• To: mathgroup at smc.vnet.net
• Subject: [mg79923] Integration of Singular function
• From: Khandelwal <ratneshk at gmail.com>
• Date: Thu, 9 Aug 2007 05:11:38 -0400 (EDT)

```Hello,

I am having trouble integrating the following functions in
Mathematica

II=Table[{t,
NIntegrate[
rf1[x, y], {y, -\[Infinity], 0}, {x, -\[Infinity], \[Infinity]},
MaxRecursion -> 60, Method -> MonteCarlo,
MaxPoints -> 500000000] +
NIntegrate[
rf2[x, y], {y, 0, \[Infinity]}, {x, -\[Infinity], \[Infinity]},
MaxRecursion -> 60, Method -> MonteCarlo,
MaxPoints -> 500000000]}, {t, 0.0001, 5, 0.2}]

rf1[x_,y_]=(0.0666667 \[ExponentialE]^-((-1 + x)^2 + (-1 + y)^2)/(4 t)
Im[((1 + 0.1516 \[ImaginaryI]) (1 + x + \[ImaginaryI] y) ((
1 + x + \[ImaginaryI] y)/(-1 + x + \[ImaginaryI] y))^(
0.0758 \[ImaginaryI]))/(-1 + (x + \[ImaginaryI] y)^2)^(3/2)])/t

rf1[x_,y_]=(0.621099 (\[ExponentialE]^-((-1 + x)^2 + (-1 + y)^2)/(4 t) -
1/3 \[ExponentialE]^-((-1 + x)^2 + (1 + y)^2)/(4 t)) Im[((1 +
0.1516 \[ImaginaryI]) (1 + x + \[ImaginaryI] y) ((
1 + x + \[ImaginaryI] y)/(-1 + x + \[ImaginaryI] y))^(
0.0758 \[ImaginaryI]))/(-1 + (x + \[ImaginaryI] y)^2)^(3/2)])/t

My problem is though i'm taking too large value of MaxPoints
(MaxPoints -> 500000000), because of that it's takes lot of time, but
still for some inital small value of t(0.0001) its not conversing. I
want to plot (t,II), where t->(0,5). Just wondering if there is other
better way of dealing this integration!!

--
Regards,
Ratnesh Khandelwal
IISc,Bangalore,INDIA

```

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