# Category:Gamma Function

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This category contains results about the Gamma function.

Definitions specific to this category can be found in Definitions/Gamma Function.

The **Gamma function** $\Gamma: \C \to \C$ is defined, for the open right half-plane, as:

- $\displaystyle \map \Gamma z = \map {\mathcal M \set {e^{-t} } } z = \int_0^{\to \infty} t^{z - 1} e^{-t} \rd t$

where $\mathcal M$ is the Mellin transform.

For all other values of $z$ except the non-positive integers, $\map \Gamma z$ is defined as:

- $\map \Gamma {z + 1} = z \, \map \Gamma z$

## Subcategories

This category has the following 8 subcategories, out of 8 total.

### D

### E

### G

### L

## Pages in category "Gamma Function"

The following 45 pages are in this category, out of 45 total.

### A

### B

### D

### E

### G

- Gamma Difference Equation
- Gamma Function as Integral of Natural Logarithm
- Gamma Function Extends Factorial
- Gamma Function for Non-Negative Integer Argument
- Gamma Function is Continuous on Positive Reals
- Gamma Function is Smooth on Positive Reals
- Gamma Function is Unique Extension of Factorial
- Gamma Function of Negative Half-Integer
- Gamma Function of Positive Half-Integer
- Gauss Multiplication Formula