## 17Calculus - Gamma Function

Gamma Function

### Resources

Wikipedia - Gamma Function

SOS Math - Gamma Function

Equations

$\Gamma(t) = \int_0^{\infty}{ x^{t-1}e^{-x}~dx }$

The gamma function is related to factorials by the fact that for positive integers, the property $$\Gamma(n) = (n-1)!$$ holds.
Here is a video clip discussing the properties of the gamma function.   This clip is within the context of Laplace Transforms but you do not need to understand Laplace Transforms in order to understand what he is talking about.

### Trefor Bazett - Properties of the Gamma Function

video by Trefor Bazett

Applications

We can use the gamma function to find this Laplace Transform.

Calculate $$\mathcal{L}\{ t^n \}$$ using the gamma function.

Problem Statement

Calculate $$\mathcal{L}\{ t^n \}$$ using the gamma function.

$$\mathcal{L}\{ t^n \}$$ $$= \dfrac{n!}{s^{n+1}}$$

Problem Statement

Calculate $$\mathcal{L}\{ t^n \}$$ using the gamma function.

Solution

### Trefor Bazett - 4377 video solution

video by Trefor Bazett

$$\mathcal{L}\{ t^n \}$$ $$= \dfrac{n!}{s^{n+1}}$$

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