1. ## Gamma functions

Hi all,

I am reviewing a section of my device physics textbook which covers the effective density of states. In the books' derivation, they reach a point where they say this:

The integral is the gamma function, with a value of

$\displaystyle \int_0^\infty \eta ^\frac{1}{2} exp(-\eta ) d\eta = \frac {1}{2} \sqrt{\pi}$

...and then jump back into the full derivation of the effective density of states (using other factors not shown here).

My Question:
Can someone please show me (in a detailed way) how they arrived at $\displaystyle \frac {1}{2} \sqrt{\pi}$? Also, in laymen's terms... what is a gamma function, and how is it advantageous? I tried looking this up, and could not make sense of what was being explained.

Thank you!

3. ## Re: Gamma functions

Thank you, but I came here because you need a PhD in math to understand either the Wikipedia entry or the Wolfram entry

4. ## Re: Gamma functions

yes you are right the gamma and beta functions are part of very advanced mathematics available to very few...
you may get some help from youtube videos like the one here:

Gamma Function - Part 1 - Functional Equation - YouTube