4
$\begingroup$

I've been having difficulties with the following question:

enter image description here

I feel this is a very simple problem that I'm overthinking, but I've been stumped on this question for a while. I've tried to simplify it and turn the integral into the gamma function, but I can't figure out how to do it! x is only present in the exp() function, so I can't understand how to transform it into something else. I would appreciate any help directing me to the right way to do this question.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
6
$\begingroup$

You're trying to use $\Gamma(t) = \int_0^\infty x^{t-1} e^{-x} \,\mathrm d x$, right? Well, not only is there not an $x^{t-1}$, the exponent has that annoying $q$ in it. Try getting rid of that problem first and then worry about the other one.

More explicit hint, click to reveal:

Use a change of variables to $u = \frac{\lvert x \rvert^q}{2 \sigma^2}$. Careful with the limits of integration when you do.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.