Definition – Gamma function – Math-reference.net

Contents
1. Introduction

1. Introduction

The gamma function is the continuous version of the factorial function. That is, the properties of the factorial function are the same as the properties for the gamma function if we only consider whole positive numbers, $n\in\mathbb{N}$ .

2. Definition

The gamma function, $\Gamma(\alpha): (0,\infty) \rightarrow \mathbb{R}$ , is defined as,

$\Gamma(\alpha) = \int_0^\infty u^{\alpha -1}e^{u}~ du$