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Integral of Maxwell-Boltzmann dist.

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data
    I was wondering if there is some sort of trick to calculate the following:
    [tex]\int{-{{e}^{-\varepsilon /{{k}_{B}}T}}}{{\varepsilon }^{3/2}}d\varepsilon \,[/tex]
    It's the derivative of the Maxwell-Boltzmann distribution, excluding the constants, times an energy in the power of (3/2).

    2. Relevant equations

    3. The attempt at a solution
    I've found the solution from 0 to infinity if the energy was powered in n (n being an integer), but I haven't been able to find anything when it's a half-integer.

    So is there some sort of trick to do this, or...?

    Thanks in advance.
  2. jcsd
  3. Apr 18, 2013 #2


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    Since integer powers are nicer why not substitute ##\epsilon=u^2##? Now you've got a gaussian times an integer power of u. That's a pretty well known problem.
  4. Apr 18, 2013 #3
    Ahhh yes, that should work. Don't know why I didn't think of that :/

    Thank you :)
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