# Gamma Function

1. Jan 17, 2009

### Gregg

I was experimenting to find out general results for various problems and found that:

$$\int Z^{yx} dx = \frac{Z^{xy}}{yLn(Z)}$$

Then I was doing a few others and thought can you do $$Z^{x^a}$$ ?

for $$x^2$$ I got a strange result, but for x^3 it seemed to be ok.

$$\left\{-\frac{x \Gamma\left[\frac{1}{3},-x^3 \text{Log}[Z]\right]}{3 \left(-x^3 \text{Log}[Z]\right)^{1/3}}\right\}$$

I've heard of the gamma function and others but have never come across it what is it. I looked it up and it says that it is, i think, the upper incomplete gamma function. I want to learn about it and other functions like it and I have a book on the Riemann Zeta function but it's quite difficult for me as i'm not even undergraduate yet. So can it be summed up in afew words or will it be better for me to go and read up about it and others in order for me to understand them better?