(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is actually part of a probability problem I'm thinking about. I'm trying to find the nth moment of a certain random variable in terms of the gamma function, which is basically equivalent to solving the following integral or expressing it in terms of the gamma function. Here is the integral:

2. Relevant equations

Mathematica:

Integrate[(a/b^a) x^(n + a - 1) Exp[-(x/b)^a], {x, 0, Infinity}]

Plain text:

integral_0^infinity(a x^(n+a-1) e^(-(x/b)^a))/b^a dx

a, b, and n are constants.

wolfram alpha:

http://www.wolframalpha.com/input/?i=integrate+%28%28a%2Fb^a%29*x^%28n%2Ba-1%29*e^%28-1%28x%2Fb%29^a%29%2Cx%2C0%2Cinf%29

3. The attempt at a solution

I tried integrating by parts, taking u = -x^n and dv/dx = ... everything else in the expression (since that can be integrated nicely using derivative is present substitution), I was left with -1 + an even nastier integral, so I'm not convinced this is the right method...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Express the following integral in terms of the gamma function

**Physics Forums | Science Articles, Homework Help, Discussion**