Find upper limit of improper integral - Numerical Integration

[architect]

Find upper limit of improper integral -- Numerical Integration

Hi,

I have the following complicated integral willing to integrate numerically. The integral is:

\int _0^{\infty }x\frac{\beta^\alpha}{\Gamma(\alpha)}x^{-\alpha-1}e^{-\beta/x}dx.

We know that the integral converges to:
((1/\beta)^\alpha \beta^{\alpha+1})/(\alpha-1).

Can anyone suggest a methodology of deriving the upper bound of the limit of this integral for numerical evaluation purposes?

Thanks for your time.

BR,

Alex

 

[fresh_42]

I'm not sure if it works, but have a look at the method here:
https://www.physicsforums.com/threads/micromass-big-integral-challenge.867904/page-2#post-5451293