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Problems on definit integratiion of gaussian profiles

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86785] Problems on definit integratiion of gaussian profiles
  • From: Regaly Zsolt <regaly at konkoly.hu>
  • Date: Fri, 21 Mar 2008 01:51:53 -0500 (EST)

Dear All Mathgroup Fellows!

I dont understand the behavoir of Mathematica integrating  
exponential functions. I try to integrate the same functions in  
different forms. The integrands are

Power[E, Plus[Times[-1, Power[a, 2], Power[c, -2]], Times[-1, Power 
[d, -2], \
Power[Plus[b, Times[-1, x]], 2]]]]

or

Power[E, Plus[Times[-1, Power[a, 2], Power[c, -2]], Times[-1, Power 
[b, 2], \
Power[d, -2]], Times[2, b, Power[d, -1], x], Times[-1, Power[d, -2],  
Power[x, \
2]]]]

which are the same, but the results will differ. Indeed calculating  
definit integral in a -Infinity to Infinity domain, assuming that all  
variables are larger than 0, the result will be completly different!

1'st case the result will be:

Times[d, Power[E, Times[-1, Power[a, 2], Power[c, -2]]], Power[Pi, \
Rational[1, 2]]]

while in the 2'nd case

Times[d, Power[E, Plus[Power[b, 2], Times[-1, Power[a, 2], Power[c,  
-2]], \
Times[-1, Power[b, 2], Power[d, -2]]]], Power[Pi, Rational[1, 2]]]

As You can see the 1'st result is completly independent of b! I dont  
understand. How can it be fixed?

Cheers,
Zsolt Regaly


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