# Gamma function

### From Conservapedia

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The **Gamma funciton** is defined as

## Relations and values

### Factorial

Using integration by parts,

At *t* = 0, *t*^{z − 1}( − *e*^{ − t}) goes to 0. Using L'Hopital's rule, it's easy to show that .

So,

- = (
*z*− 1)Γ(*z*− 1).

Thus,

- Γ(
*z*) = (*z*− 1)Γ(*z*− 1).

Using this, and the the fact that Γ(1) = 1, then we can get the factorial function. For *n* a positive integer,

- Γ(
*n*) = (*n*− 1)!.

### z=1/2

For z=1/2,

Substituting *x* = *t*^{1 / 2},

where in the last line we used the fact that is an even function. The integral is called the Gaussian integral and has a well known value of .

Thus,