Integral of an involved exponential

[singhofmpl]

Homework Statement

I have problem solving an integral equation of the form

Homework Equations

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

The Attempt at a Solution

I have tried to solve it by substituting $$t=\frac{\Lambda\gamma}{\Gamma (\gamma-\Lambda)}$$ and able to bring it to the following from:

$$\int_{0}^{\infty}-a\exp((c\Gamma t^2-(c\Lambda+\Lambda\Gamma-b\Gamma)t-b\Lambda)/(c(\Gamma t-\Lambda)))dt$$
but I'm not able to move further. Any suggestion to solve this integral will help me a lot.

 

[phyzguy]

What is $$\Gamma$$? 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 $$\int_0^\infty \frac{e^{au^2}}{u}du$$. This has a solution in terms of the exponential integral (Ei).