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Homework Help: Integral of an involved exponential

  1. Jun 7, 2010 #1
    1. The problem statement, all variables and given/known data

    I have problem solving an integral equation of the form


    2. Relevant equations

    [tex]\int_{0}^{\infty}(a\Lambda^2/(\Gamma(\gamma-\Lambda)^2))exp(\Lambda\gamma/(\Gamma(\gamma-\Lambda))-(\gamma-b)/c)d\gamma[/tex]

    3. The attempt at a solution
    I have tried to solve it by substituting [tex]t=\frac{\Lambda\gamma}{\Gamma (\gamma-\Lambda)}[/tex] and able to bring it to the following from:

    [tex]\int_{0}^{\infty}-a\exp((c\Gamma t^2-(c\Lambda+\Lambda\Gamma-b\Gamma)t-b\Lambda)/(c(\Gamma t-\Lambda)))dt[/tex]
    but I'm not able to move further. Any suggestion to solve this integral will help me a lot.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 7, 2010 #2

    phyzguy

    User Avatar
    Science Advisor

    What is [tex]\Gamma[/tex]? Is it a function or just a constant? If it is just a constant, you should be able to do a further substitution and complete the square inside the exponential to get it into the form [tex]\int_0^\infty \frac{e^{au^2}}{u}du[/tex]. This has a solution in terms of the exponential integral (Ei).
     
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